I wanna know what the deal with shoe sizes is.

Shoe sizes are a mess. Units are a mess. Matt proposes a system: Measure the foot length and width in mm, rounded to half centimetres. Matt discovers that this system is also called Mondopoint. [Editor's note: The Mondopoint system is standardized by ISO 9407.] Listeners are invited to embroider (or write with permanent marker) their Mondopoint shoe size onto their shoes. Matt promises to send the first listener who sends a picture of an embroidered shoe a signed copy of his book.

A "ting" by Bec

What is the most number of my own organs I can sell for the highest profit without dying in the process?

You can live with only 45% of your own body mass, but don't try this at home. If you sold all those body parts, you could make just over £900'000. You can also sell blood, plasma, hair, sperm, eggs, bone marrow, breast milk, faeces, urine, or be a surrogate mother. Bec's on a list now and her search history is ruined forever. Oh, and she buys human teeth from adult humans for £2 per tooth (£5 or a pint for a wisdom tooth).

None, but Bec says "So that's all the problems solved in this first episode" at the end of the episode, which I consider an implicit ding

Given the general cost of running a fridge is the electricity, and that they're continually becoming more energy efficient whilst electricity becomes more expensive, how often should one buy a new one?

If you've got a fridge from the 90s, you'll make your money back in 3.5 years. If you've got a fridge from the 2000s, it'll take 7 years. Don't even keep the old fridge as a second fridge, buy a new one. But if you buy a new one now, it'll probably last you for a few decades.

A "ka-chiiing" from Bec

Matt needs to buy Christmas presents for his nieces (7 and 9 years old) and needs cool gift ideas.

Idea 1: Harry Potter invisibility cloak (£60), a cape that's green on the inside for use with a green screen.

Idea 2: Scruff A Luvs "My Real Rescue", an electronic toy dog that emulates a rescue dog.

Idea 3: smART pixelator (£50-£70), beads and an app that pixelates images for use as a template.

Idea 4: Oculus Quest (£400-£500), a VR headset. This one might have been from Bec's Christmas list.

Idea 5: LEGO Mars Research Shuttle (£20).

A "That, Bec, is a problem solved" by Matt

How much pizza is too much pizza?

Bec decides the standard unit of pizza measurement is a large (14 inch) Domino's Classic Crust Cheese Pizza. It's about 1000 g, which is about 1 l, which is about the volume of the stomach of a non-competitive eater.

Bec asks comedian and doctor Kwame Asante, who notes that you'll die if you consistently eat too much pizza. Bec and Matt decide that the problem is about a single session, and discuss symptoms of overeating.

In 2018, Geoff Esper ate 19.25 9 inch pizzas in 10 minutes, which is almost 8 large pizzas. However, in a twitter poll by Bec, 45% of people say they only eat one pizza.

Given these inconclusive results, Bec and Matt decide on an experimental approach and Bec orders one standard unit of pizza per person. The conclusion: Too much pizza is between 3/4 of a large pizza and one large pizza in a sitting.

A "ding" by Bec

What is the mathematically optimal way to store shirts, in terms of volume used? Folded, rolled, hung up, or some other method?

Matt and Bec practice experimental mathematics with a lot of Matt's nerdy T-shirts and an (initially) empty box. While Bec rolls shirts, Matt explains that his ideal T-shirt storage system should be FIFO (First In, First Out). Bec explains her coat hanger system for tracking worn clothes. Matt debunks the penny pusher T-shirt drawer setup.

Experimental results: The box fits 15 rolled, 12 folded, and 9 scrunched-up T-shirts. While hung-up shirts win for FIFO purposes, rolling is the most volume-efficient.

A "problem solved, ding" by Bec

Matt has never gotten the hang of jet lag. Does Bec have a solution?

Matt is travelling from the UK to the US soon. Both Matt and Bec regularly travel between the UK and Australia. Matt and Bec both originally come from Australia but live in the UK.

Shift-worker syndrome (e.g. from a night shift) is the same thing as jet lag. You can buy melatonin, but it doesn't solve the jet lag itself, just helps getting to sleep. Hangover and jet lag are similar: Not sleeping and hydrating properly.

Bec suggests moistening clothes in the in-flight bathroom. It helps with dehydration, and people won't want to sit near you, which gives you space to sleep. Matt will give it a go on his flight and report back.

Is 2020 the start of the new decade or the end of the previous decade?

Bec retweeted a thing of the decade, someone else replied and was angry, so Bec roped Matt into it. People on both sides yelled at Matt. Matt and Bec discuss twitter and go on to reinvent 90's forums.

There is no year 0, 1 AD immediately follows 1 BC. This is different from birthdays: When you're n years old, you've been out of the womb for n years (and a bit). When it's the year n though, there have only been n-1 years (and a bit). This means that the first 10 years, i.e. the first decade, starts at the beginning of year 1 and ends at the beginning of year 11. However, decade names like "the 20s" count the years starting at 2020.

Matt goes on a tangent of saying "zero" instead of "oh" in phone numbers. In the book 1984, there's room one-hundred-and-one. James Bond is Agent seven, the lead zeroes are unnecessary.

The International Standards Organization (ISO) released ISO 8601 (eight-six-zero-one), the official standard for dates and times. They ruled that 1 BC is year 0 and 1 AD is year 1. This means our decade started in the year 2020. What pedant can argue against that?

A "ting" by Bec

Now that you've eaten too much pizza, what is the optimal sequence for brushing teeth? Upper before lower? Left before right? Insides before outsides? Working in quadrants? Could electric brushes require different sequences to ordinary brushes? Does the amount of viscosity of the toothpaste play a factor?

The sequence doesn't matter as long as you're brushing them equally. Most tooth-related organizations say you should brush in quadrants, for timing: 30 seconds per quadrant, 2 minutes in total. Matt worked this out on his own from his electric toothbrush, which, by the way, are not faster than manual brushing.

Matt worries that always starting in the same quadrant has a negative effect and instead rotates his starting quadrants. Sources online surprisingly don't mention this, though Bec guesses this has no effect.

You only need a pea-sized amount of tooth paste, more doesn't help. Just make sure it contains fluoride. Also, spit but don't rinse, and don't use mouth wash for at least 30 minutes after brushing. You don't want to remove all the fluoride again that you've just put on your teeth.

A few more tips: Brush your tongue too, lots of bacteria on there. Floss before you brush, so you brush away the dislodged detritus. Wait at least 20 minutes after eating before brushing, because acid in the food softens your enamel.

If you want to speed-run brushing, you can try an Amabrush, a brush that looks like a mouth guard and brushes all your teeth at the same time in 10 seconds. Sadly, it's a kickstarter and they seem to have gone bankrupt. Instead, Matt suggests one electric toothbrush per hand, working on diagonally opposite quadrants at the same time.

Addendum by Bec's friend Sophie (a professional dentist): The starting quadrant does not matter, the toothbrush only removes plaque. Brush your gums as well, plaque likes to accumulates between teeth and gums. Tooth paste saturates the saliva with fluoride, calcium, phosphate; the saliva then washes it over the teeth. This process takes time, so spit, don't rinse, wait 30 minutes. One of the manual brush techniques mentioned was called the "bass" technique. If you must use mouthwash, use it before brushing.

A "ting" by Bec

The premise of Bec's show "Out of Order" is that the jokes are on 25 post-its on a board and the audience gets to pick the order. What is the maximum amount of times Bec can do this show before she hits the same order again?

There are 15'511'210'043'330'985'984'000'000 (15.5 septillion) distinct orders: At the beginning, there's 25 options for the first joke, then 24 for the second, and so on, which makes 25*24*...*1 = 25! ("25 factorial") joke orders. If the audience chooses at random, you have to do roughly 500 billion shows before you hit the first repeat order (on average). Matt requests Bec to log the order of each of her 25 or more shows, so they can analyze the results afterwards.

A "ding" by Bec

A "So you did, you solved the problem" by Matt

What happens if you actually get quarantined in a hospital? What do you take? What goes on? Any recommendations?

There's not much, only a bed, bathroom, sink, and a window (nature's TV). Chances are you're so sick you don't need anything else. Don't worry too much about entertainment. Take a tooth brush, tooth paste, toiletries (if you have preferred ones). Take a couple of pairs of socks and a spare blanket. Take a pair of normal clothes for your way home. Maybe a friend who can drive you back and then leave the car for two weeks.

They gave her a phlegm flask to collect samples from violent coughing. Take some fun item to put in there, maybe a lego figurine, dnd miniature, a small vial of Worcestershire sauce, or wasabi. When hospitals are overloaded, all the staff want is a little laugh (at least according to Matt).

"[…] while the virus is still alive." — Bec

A "ding" from Bec

What are Matt and Bec's tips for working from home?

Keep in touch with other people, but don't over-socialize too fast. Maintain a certain routine. Bec is recording this episode from a small closet under her neighbour's stairs, by the way.

Bec's routine: Bec has a big whiteboard with a check list which she has to complete every day. First, she writes a few pages stream-of-consciousness, for mental health purposes. She has a stay-focused app that blocks messages before 10:00 and after 22:00. One of the items is "go outside".

Matt's routine: Matt refuses to look at the emails before he officially starts work. After Matt and Lucie get ready, they walk to work by walking around the block once (a 20 minute walk). At the end of the day, they walk the other way back around the block.

Bec challenges people to recreate the dance from Iceland's Eurovision entry "Think about things" to get exercise instead of going for a walk at the same time as everybody else. Matt will not participate.

Matt's tip for getting up at a reasonable time: Have a proper schedule that doesn't make you get to bed late. Bec's advice for staying focused: Don't talk to her. Create a dedicated work space or corner. Bec has a working nook in her kitchen. Listeners are encouraged to send pictures of their own workspaces.

A "ding" from Matt

Bec has been seeing a lot of memes and infographics, and she doesn't know which ones to believe. Bec describes a specific meme titled "The power of social distancing" that shows significant decrease in infections when exposure is reduced.

Matt looked up the source of the meme, which appears to be reputable. He then reverse-engineered their calculations, which appear to be sensible. Some infographics count the currently infected cases, some (like this one) counts the total amount of infections.

Two things are scary about exponential growth: First, a slight difference in the infection rate has a large effect on the end result. Second, it starts deceptively slow but in the end grows very large very quickly. As an example, Matt fills all the houses in the UK with rice in one month.

A "ding" by Bec

By Manic

When episode 003 was released, a lot of listeners replied they couldn't hear Bec, or she was very quiet, or she felt very far away. Some said she was phoning in from the ISS.

Producer John Harvey explains that Bec's waveform was out of phase and had to be flipped. Flipping a sound wave just inverts the wave form. Adding opposite sound waves cancels them out. This is the idea behind noise cancelling headphones, and can also be used to remove vocals from songs.

Using the phase of the audio and weird combinations of the channels, an approximation of surround sound can be encoded in stereo channels. This is called Matrix Decoding.

A link to the broken episode can be found in the show notes. Listeners are encouraged to play it on a variety of weird devices. Bec also provides a weird audio file that has caused problems with some venue audio setups.

A "ding" by John

If you're on a crowded tube train with a backpack, where is the best place to put it? On the floor, people assume it's a space to stand in. In my hand, it lurches into people. How can I get in people's way the least?

Bec likes big backpacks and cannot lie them on the ground in the tube.

Solution 1: There need to be dedicated backpack carriages for backpackers where half of people are really tall and the other half is short. Alternatively, put some people in upside-down like Tetris.

Solution 2: Wear the backpack on your front, put your clothes over it, and wear a "baby on board" badge. People will stay clear of your bag and you might even get a seat.

Bridget gets to decide whether this solves the problem.

As an air traffic controller, I am bound by certain restrictions for safety: 5 nautical miles laterally, and 1000 ft. Which, let's be honest, is a lot of room. Go out and run 5 miles. That's how close I'm allowed to have two aircraft at the same altitude. That's a ton of space, right? I could easily fit more in there. But then I wondered: How much more? So my question is: In a 3-dimensional space with a radius of 5 nm and 1000 ft high, just how many airplanes could I cram in there and have none of them touching? Not travelling per se, but a frozen snapshot in time, assuming each aircraft is a Boeing 737, for sake of measurement ease. Thanks!

Matt commends the level of precision and detail in the question. However, Matt did not run the 5 miles. The described volume is a cylinder. While one might think the cylinder would be 2000 ft high, the question was very clear about its height.

Matt builds an aircraft cake with 24 layers and 177'987 planes per layer, for a total of just over 4.2 million planes. If you interlace the wings, you can fit approximately 6'334'728 planes instead. This is a packing problem, which are notoriously difficult. You might fit even more by computer simulation. Nowhere in the question does Rob state the aircraft needs to be intact, so you could fit even more by compressing them.

However, the aircraft has only been ordered 15'115 times, of which 10'575 have been delivered. So the actual answer is just: All of them.

A "ding" by Bec

In my house, Matt has a spare guest bedroom. What has to happen to make that the perfect guest bedroom for people who stay over? Current inventory. Bedside table with a lamp, USB power outlets built into the wall socket. And a bed.

Suggestion 1: Get rid of them boxes.

Suggestion 2: If you expect people to stay for a few nights (which is not the case here), a space to hang and put clothes.

Listeners' favourite things in their bedrooms: A bed and comfortable mattress (which is already in place). A (cuddly) toy or figurine, possibly puzzles. A quilt. A partner (Lucy?). A pet (including kids; befriend/steal neighbour's cat). A Spider That Lives In The Room And Catches Flies. A Star Wars pillow case. A butt (by Picasso). A Bec shrine (or for the specific guest).

Bec provides Matt with a futuristic garden. It's a toy, but has live, so it's a pet, and it's space-related, so it's related to Matt's partner.

A "ding" by Bec

Bec has found an old white T-shirt that she wants to divide into 500 regions. People can pay £10 for her to draw or write something in one space. How should she arrange the 500 regions on the shirt?

Old Man Matt reminisces about the Million Dollar Website. Since Matt didn't answer in time because he didn't have an off-the shelf cauldron ready, Bec also asked her little brother Mike. Mike computed that each section should be about 4 cm by 4 cm in size. However, he did not figure out how to arrange them, which Matt did.

Matt wrote some Python code and checked 5'904 different square arrangements (not including sleeves). Optimizing for area, the best solution is a lot of very thin regions. With some manual sorting, Matt's favourite solution was: 3cm wide by 2.1cm tall, on the front 20 wide by 23 tall, on the back 10 wide by 27 tall.

Bec changed the shirt size, which Matt accounted for in his code. The code is taking quite a while though, so they decide to do another problem first.

What portion of the energy that goes into a clothes dryer ends up trapped as static electricity on the clothing?

It takes about as much energy to run a clothes dryer for an hour as does running a human for a day. According to regulations, the maximum percentage of that energy that may be static charge is 0.00000324%.

The code from problem 006-1 is still running.

A "ding" by Bec

What do the numbers on a toaster mean? Is it minutes? Would setting your toaster to 5 burn your house down? What happens if you set your toaster to 1 but a few seconds later you change it to 3? Does it let you change it? What happens if you set a toaster to 5 but you wait until it's around about the 3 level of cooked and then turn it down to 1? What would happen? What if you have a four-slice toaster with two levers but one dial, and you set the dial to a 3 and push down the first lever, and then halfway through you push down the second lever?

Bec checked a video by Tom Scott (recommended by Matt) who tested what the numbers on toasters mean. She then reached out via Twitter and @press_coffee and @regularlods [Editor's note: I could not find the second account, and might have misheard the name] who helped with experiments with their own toasters.

What do the numbers on a toaster mean? Is it minutes? The numbers don't mean minutes, and it's not even a linear scale.

Would setting your toaster to 5 burn your house down? Depends on your toaster (the podcast doesn't have insurance to find out an actual answer).

What happens if you set your toaster to 1 but a few seconds later you change it to 3? Does it let you change it? Experiments verify that different toasters do different things.

What happens if you set a toaster to 5 but you wait until it's around about the 3 level of cooked and then turn it down to 1? What would happen? In every case, the toast popped up.

What if you have a four-slice toaster with two levers but one dial, and you set the dial to a 3 and push down the first lever, and then halfway through you push down the second lever? Limmy replied they have a four-slice toaster, but they'd prefer the mystery and don't want to know. If anybody works out the answer: Don't tell Limmy! Instead, say: "I watch Limmy's show thanks to A Problem Squared, and really enjoyed it."

By Bridget B

What is the biggest thing in Australia based on scale? In other words, what is the biggest in comparison to what the normal thing should be? What is the funniest if you're going solely on "unexpectedly big" on scale?

First, Bec and Matt ramble a long time about unusually sized objects, including a pair of children's size roller skates and a reference to problem 001-1.

Matt found 249 big things in Australia. The most common big thing is apples, the biggest of which is about 5 m tall. Things that are smaller than they should be are the Big (map of) Australia and the Big Ayers Rock.

Contenders for the answer are the Big Ant, the Big Macadamia Nut, the Big Olive, and the Big Redback Spider. They're all about the same scale factor, within rounding and guessing errors. Bec chooses the Big Macadamia Nut, which is in proximity to a Big Pineapple. Listeners are encouraged to send pictures of themselves with a big thing.

A "ding" by Bec

Person 1 asked: If you're an average person, could you win the lottery and retire, or is there not enough money? Person 2 asked: How much do I need to save for retirement? I know what financial people say, what do maths people say?

Matt combines the questions into "If you won a million dollars, would that be enough for retirement?" and interpreted "retirement" as "30 years". That makes $33'000 per year. With inflation, that will be roughly $11'000 after 30 years, so you need some sort of investment that matches inflation.

Legally, Matt can't give financial advice, but he had a look at stamps: In the UK, some stamps don't have a value on them, but their price increases occasionally and they don't expire. The stock market gives a better return on average but is also a lot more dangerous. You could also buy an annuity and not rely on the postal service continuing to exist. Some lotteries also offer an annuity as a reward.

So maths people say "listen to the financial people" and Bec says "give it to me".

A legally distinct "dong" by Bec

Deemed "too ridiculous to solve" by Matt

My brother keeps complaining about a situation he and his wife are in. Namely, he's pretty tall and she's definitely short, and neither of them like using the kitchen counters because the average height that they are designed for is uncomfortable to reach down to or reach up to respectively. How can I get him to stop complaining to me about this problem or — even better — what could they do to solve their kitchen height woes?

Bec suffers from an optical illusion where people assume her to be smaller than she actually is, and her husband Gavin is very tall, so she can emphasize. Her solution: Her husband does all the cooking.

For a more practical solution: Bec asked her friend and comedian Gareth Berliner, who is married to Kiruna Stamell who has dwarfism. He mentioned rise and fall counters, which are counterweighted and can change their height. Bec contacted Ed Warner, whose company called Motionspot makes well-designed accessible counters. He explains the different types of furniture they offer.

To stop the complaining, Manic should get their brother to listen to this episode (as should people with similar problems).

A "I think I can confidently give that a very firm ding" by Matt

My question is truly global: I'm wondering whether the recorded area of each country — as stated by encyclopedias etc. — assumes the country is completely flat/completely smooth, i.e part of the surface of a sphere, or takes into account topography. For some countries, e.g. the Netherlands, there might be little difference between these figures. But for others, e.g. Switzerland or Norway, the many steep mountains could surely make a significant difference. Any idea which country would exhibit the biggest difference, and whether it would be enough to change its place in the traditional ranking of countries by land area. Thanks!

Matt likes the problem; Bec wonders if Phil has land investments. For tides at coasts, you use the mean high water mark as a defined border. Matt explains the coastline paradox, where a coastline is fractal and its length changes depending on the granularity in which you measure it.

Matt could not find out who's in charge of the UK's surface area, so he looked at Australia (which is about 31 UKs in size), for which Geoscience Australia is responsible. Matt struggles with their geo data format. Geoscience Australia confirms that they don't include height in their computations. Matt extrapolates that this applies to all countries.

Alistair Ray [Editor's note: Spelling likely incorrect] has previously tried to answer this question using a 25 km² chunk of Scotland. However, the same coastline problem now applies to the 2D surface of the land: The higher the resolution of your data, the higher the surface area. The 25 km² area in Scotland increased by 7.1% to 8%. Switzerland increased by 6.96%, Liechtenstein increased by 8.72%.

Matt will keep working on this problem and plans to release a YouTube video on the standupmaths channel at the same time the podcast is released. Bec only gives it a "di", the "ng" will be awarded when the video is released

Problem: Why don't plastic things dry in the dishwasher? Why? Whyyyyyyyyyy?

Bec has no (electric) dishwasher; Matt is a big fan of them. Matt experimented with his dishwasher earlier before recording, which opens itself slightly once it's finished. He guesses it has to do with the heat capacity of the materials (i.e. how easily they warm up or cool down). Matt suspects that Plastic has a lower capacity, thus cools down quick and doesn't dry well, while ceramics retain heat longer. Lucie suspects surfactants in the detergent, which change how the water interacts, beads, and drains off. Bec suspects plastic containers are usually containers, which would trap steam better. Their theories run into more and more troubles with differently-shaped and -materialed kitchen implements. Listeners are encouraged to do their own experiments and report back. Dish washing experts are also encouraged to get in contact.

Andrew retweeted a tweet by @dumbbass: "We need to melt down all the pennies and make the Statue of Liberty a girlfriend." Andrew then asked: Would the resulting girlfriend be far too big, far too small, or sort of about right?

Matt agrees that the penny should be abolished, and would strategically pay with cash or card so the rounding would be in his favour.

There's currently 130 billion pennies in circulation in the US. Using only their copper, you could make 81.25 statue of liberty sized girlfriends, or one girlfriend that's 9 times as big. The zinc from the coins is not a structural material.

Matt recommends that, after pennies are abolished, the next year's worth of materials should be turned into a statue. This statue would be within 10% of the Statue of Liberty.

A "ding" by Bec

Yo, I love burgers, but people keep making 'em too tall and I can't fit them in my mouth. Question: For a standard human jaw, what is the upper limit of burger height such that you can bite through top to bottom in one chomp?

The average human jaw can open roughly three human fingers wide. If you can't fit more than two and you go for surgery, you need to let your surgeon know. So your burger should be at most three fingers high, or two if you want to be careful.

To experimentally verify her results, Bec spent all of Saturday ordering five of the tallest burgers she could find. A video is available on her YouTube channel. The biggest burger was 10 cm high compared to Bec's 5 cm high mouth, and even with her special burger hooking technique, she did not manage to get a bite. Meat burgers can be compressed to approximately 80% their original size.

Matt dislikes tall burgers: Your burger should not need a load-bearing skewer to stay in place. Also, making your burger wider is a more efficient way to gain volume. Matt also accepts cutting a burger in half like a sandwich, but Bec vehemently disagrees.

The twitter account seems to have only ever asked this one question, and was later suspended for violation of twitter's rules.

Keeping cool in the non-air-conditioned home office: When opening a window seems to let more heat in than cooling breezes, what's the best way to keep cool whilst working at home?

Advice 1: On hot days, keep your curtains closed.

Advice 2: Buy a fan or an air conditioner. If you only have a fan, point it blowing over a bowl of ice, or drape a wet towel over yourself and sit in front of a fan.

Advice 3: Cover yourself in minty shower gel.

A "ding" from Bec

Tristan made a detour and visited the Big Macadamia Nut from problem 007-1. He'd like to know what the value of the Big Macadamia Nut would be, monetarily, if it was an actual nut.

The nut may be 640 times bigger than a normal one, but if you wanted to fill it, you'd need 242'144'000 normal sized nuts because the volume grows with the cube of the size. Those would be worth 11'796'480 AUD, or roughly 12 million AUD, or £6.5 million, or $8.5 million, or 7 million €. You'd have 865 tons of edible nut bits. Awaiting a reply from Tristan.

Hey Bec and Matt - I'm moving into a new house soon and I have this problem that I need solving. This house has one additional room that I don't need (an entirely new issue for someone who has lived in high cost of living cities - Sydney and London - for their whole life). What should I do with this spare room?

Bec's suggestions: Turn it into a secret room with a disguised door, for all your secrets. Also, get a Murphy bed (fold-down bed) for the room, so it can be used as an emergency guest room and Matt and Bec can visit. Bec goes on a diversion on animal crossing pocket camp. She suggests Mike to get a hobby and fill the room with related items, or to find a person that needs a room and give it to them. Awaiting a reply from Matt. Listeners are encouraged to send pictures of their own secret rooms.

Since episode 1 is when the podcast starts, is this an n-out-of-n+1 thing as 12 months ends at the 13th episode as there is a month between each episode?

Does the goal of 100 patrons after one year from episode 003 (note) apply in episode 012 or 013? Matt counts the month leading up to an episode as the month of the episode (the producers' perspective), while Bec counts the month after the episode (the audience's perspective). Taking both perspectives into account, there's 13 months in a year. Matt proposes a linear fade-in during the preceding month and a linear fade-out during the succeeding month, keeping the total amount at 1 the entire time. Awaiting ding from author.

Previously, Bec and Matt talked about a Ferrero Rocher pyramid from a classic commercial. How many Ferrero Rochers do you require to assemble a platter of the proportions as seen in the commercial?

@setalyas on Twitter used a circle-packing website to work out the amount of Ferrero Rochers. Packing smaller circles into a big circle is a really hard problem. Matt bought almost hundreds of Ferrero Rochers with his Seth Myers consultancy money to verify the results experimentally. After a lot of trial and error, Matt has successfully stacked the balls, though he has not counted them. Matt promises to lend Bec his sweets after counting, so she can have a go (and definitely not just eat them all).

"The outer layers are a manifestation of what's going on inside" — Matt Parker, 2020

Follow-up problem: Is 216 chocolates spoiling the people? Bec used her new ambassador powers to guess that there are about 200 people. Matt notes that having exactly as many sweets as guests is top-tier ambassadoring. Bec suggests that only one sweet per person is spoiling their fun.

Matt calculates that the maximum number of Ferrero Rochers in a pile before it collapses under its own weight, based on his own measurements, is 68'814'850 Ferrero Rochers in 650 layers, costing just over £26.25 million.

How do we determine when an area changes name based on volume? At what point does a room become a great room? At what point does a great room become a ballroom? When does a ballroom become a great hall? And in the other direction: What about a hallway? At what point does a hallway become a room? And when does a closet become a room? Is it number of doors?

Number one: What makes a room a room is whether it can fit the thing that the room is named after. A closet can't fit a bed, so it's not a bedroom.

Number two: The word "hallway" comes from "hall", which was a large building. It is also a room, but with lots of doorways to other rooms going off it. Its name doesn't change based on its volume.

Number three: A room becomes a great room when Bec Hill is in there.

A "problem solved, ding, bye" from Bec

Sharks constantly grow new teeth. What is the fastest rate you can pull their teeth out so that they always have at least one tooth (assuming one tooth at a time)?

Bec likes this problem because of her obsession with teeth, described in problem 001-2. Shark have a conveyor belt of teeth in their mouth. Nobody really knows how many teeth shark have, or how fast they regrow. Bec's best guess is anywhere between a day and a few weeks. She that sharks have roughly 49 teeth in their outer layer, and that each tooth is replaced once a week, which makes a tooth every three or so hours, or every hour during working hours (including weekends), but you take lunch time off.

A "ding" by Bec

I have a question: A lot of people are infected with covid, but a virus is also very small. That made me wonder: How many litres of the virus are there? I guess it can't be that much.

A cell is about 10'000 times smaller than a human. Bacteria are about 1000 time smaller than our cells. A virus is around 1000 times smaller than bacteria. Matt estimates one virus to be 150 nm across. Scientists estimate 400'000 viruses per ml of fluid. Matt estimates 2 l of said fluid per infected person, 300'000 new cases per day, and an average infection length of 2 weeks, meaning there's just over 4'000'000 people currently infected.

Combining all that gives us roughly 3.3 quadrillion (3.3e15) virus cells. Stacking them like tiny Ferrero Rochers (see problem 011-2), this gives us roughly 8 ml of virus, about a teaspoon. No matter how you tweak the numbers, it'll fit into a shot glass.

Footnote: Even though virus particles are tiny, it's still worth wearing a mask. The viruses in the air are carried by substantially bigger droplets.

An "I'm happy with saying that's definitely a problem solved" from Bec

I used to think of big fluffy jackets as being inherently warm, but of course they're really just insulation against the cold. How hot does it have to be outside before wearing a jacket will help you stay cool? Does it depend on how long one spends in the heat?

Our core body temperature is around 37°C, Bec's slightly cooler 🕶️. Naïve answer: At any temperature above 37°C, the jacket insulates us against the outside heat. But biology is a lot more complicated. The body constantly generates heat, and the jacket will prevent sweating.

Bec was confused by firefighters and their calendars, so she asked Dr. Rohan Francis, who then asked a firefighter. The jackets allow the firefighters to walk through flames, but only for a certain amount of time.

Bec has access to both a fluffy jacket and an infrared sauna for experiments, but she is not sure how to experiment. She asks listeners to contact her with ideas.

I recently bought Cheese in Tesco's in a more unconventional shape. Tesco claims that this squarer packaging uses 40% less packaging than its previous rectangular block. [The author forgot to measure an old block of cheese for comparison, but includes measurements for the new block.] Firstly, is Tesco correct in saying there's a 40% reduction in plastic? What would be the most efficient packing solution that minimizes wasted space and cuts down on plastic? Which products would have the greatest improvement in reducing packaging by just changing its shape?

Matt does not think there is a sensible shape for the old packet that would lead to a 41% reduction in surface area. The only real option would be a large thin pancake of cheese, which seems unrealistic. There must be something else going on.

The best way to package would be a cheese ball 9 cm across. A sphere has the smallest surface area of all shapes. However, wrapping and stacking them becomes worse (as discussed in problem 011-2). So instead, Matt wants a shape that stacks well but minimizes surface area, which is known as the Kelvin problem. Lord Kelvin claimed in 1887 that a truncated octahedron was the optimal shape. In 1993, he was proved wrong with a weirder shape.

But for transport in a cuboid box, you want a cuboid shape, so Tesco's approach is actually the right one. Matt suspects that optimizing the shape for transport might be a bigger deal than the actual amount of plastic, but that's hard to describe on a block of cheese.

Matt Bec suggests contacting Tesco's. wants to measure some cheese. Listeners are encouraged to ask Tesco's as well. Bec suggests the hashtag #cheesecoverup.

Matt wants to send out christmas cards for patreon supporters of the podcast, but he doesn't know what to put on them.

Matt has sent math-pun-ish christmas cards to his patreon supporters for the past four years, which he shows Bec. Since the podcast patreon goal (from episode 003 (note)) was met, he also wants to start the same tradition for this podcast. He requests help from Bec for christmas card ideas. The new patreon goal for the next year of APS will be 314 patrons, or roughly pi hundred.

I'm living by myself three floors up without an elevator, and I often find really nice furniture outside that I can't take because I can't carry them up the stairs by myself. Is there a most efficient way of carrying something big and heavy upstairs in terms of how much energy one has to put into it?

Matt's Step And Conquer gazebo from problem 004-2 was damaged in a storm, but he found another identical gazebo being thrown out at the same time and used it for parts.

Matt calculates that the weight of the object decreases very slightly as you go up higher. Bec suggests to flood the stairway and utilize buoyancy. Matt suggests an online calculator for how many helium balloons you need to hover an object. Matt also suggests a pulley system, but is not responsible for any damages caused.

Bec has five suggestions for getting someone else to do it: Dress like a little old lady nun and look like you're struggling, convince some passing children that it's a game, design a fake VR game about moving furniture and call for beta testers, get an ACME catapult or trebuchet, or leave it in the street for Bec's mum to trip over, and she'll put it away.

Bec also veers dangerously close to practical advice with a sack trolley with three wheels that are optimized for stairs. She contacted Luka Muller from the "Oooh, Spooky" podcast who is a professional removalist, who recommends a manoeuvre called the "lover's shelf" or the "mover's g-spot" where you rest the edge of an object in your hip groove (mons pubis). You'll look like you're humping your furniture though.

A "ding" from Bec

"He has a weak constitution" says their birthday is coming up and asks: I don't want anything. People insist on getting me something. What do I ask for? It must be a physical item.

Joanna Williams asks: With christmas looming, I want to do some nice stuff with my boyfriend and for my family, but I don't have a lot of disposable income [Matt: and with the second lockdown, we're obviously limited in what we can do].

Call their bluff and request something hand-made, or hand-make something for your giftees.

Bec suggests a recipe for fudge, full recipe in show notes. Matt mentions a custom spice mix and honey from hobby beekeeping. Bec suggests salt dough, which is basically custom Play-Doh that you bake to make solid. Matt makes candles from other candles' wax. Bec suggests a treasure hunt advent calendar with 25 clues. Listeners are encouraged to share more ideas on instagram.

Another option: Ask for a physical item that helps other people. For example, a product from a company that donates a part of their proceeds.

A "ding" by Matt

A "Ding, dingalingaling" from Bec

What exactly defines the difference between a biscuit and a cookie?

Bec says they're the same thing, just a language difference between the states and Australia. Matt notes they might be different in savouriness. Both argue, wasting precious time. John Harvey asks whether the cookie monster would eat a digestive biscuit, Matt suspects yes.

A ding from Jon Harvey

The "fact" that 63 Earths can fit inside Uranus doesn't make clear whether this is a simple volume comparison or whether it's considering sphere packing. Can you shed any light?

Matt previously looked into this, and the answer is: 63 without sphere packing, only 46 with sphere packing. The fact ignores sphere packing. Bec keeps giggling the whole way through.

A "ding" from Jon Harvey

I've never found a four leaf clover. Can you tell me why it is so and how to tip things in my favour?

Bec calls Luke unlucky. Matt points out that the causal direction should be the other way around: Clovers should make you lucky. Matt also recommends searching near Chernobyl.

A "ding" from Jon Harvey

Is the show title "A (Problem)(Problem)" or "(A Problem)(A Problem)"?

"Correct, the title is a problem." - Bec

Matt is fascinated by how people read mathematical equations. He argues that a Mathematician would say "a problem, all squared" for the second case. He parses the title as "A (Problem)(Problem)".

A "(ding)(ding)" from Jon Harvey

If you had a donut shaped planet, I assume that if you went to the center hole, you would experience gravity pulling you to the planet. So, what would happen if you went to the center of the Earth? More gravity being pulled to the surface, or no gravity?

If you were in the middle of a toroidal planet or the Earth, gravity would cancel out. If you're anywhere inside a hollow sphere, no matter where inside the shell you are, everything still cancels out perfectly.

"Well, cause gravity definitely works with my hole." — Bec

A "ding" from Jon Harvey

A "That is definitely a problem squared" by Matt

Catherine wants to know if it's possible to cast shadow puppets on the Moon via their house.

Question 1: If it is possible, how big would their hands and torch have to be to cast shadows?

Question 2: Is there a certain place on the earth that works best? Catherine lives in Cheltenham (UK) and wants to know if she should consider moving.

Question 3: If she is standing on Earth with the right equipment, is the distance too great to cast accurate shapes? Would the shadow puppet just become fuzzy beyond recognition?

Question 4: What's the best time of the month or year to do it?

The Moon is a long way away. Bec theorizes that people judge the Moon's size like they judge Bec's height: Always a little too small (which she previously complained about in problem 008-1).

Answer 1: Since the moon is about 100 times as far away as it is large, puppets would also need to be 100 times as far from the torch as they are large. The torch does not need to be massive. Bec realizes that a solar eclipse is just the Moon playing shadow puppets on the Earth.

Answer 2: Stars twinkle because the atmosphere is like a giant instagram filter. Astronomers choose locations that have the fewest cloudy days per year. Curiously, those conditions also make for great holiday destinations... The less atmosphere the better; ideally Catherine could move above the atmosphere.

Answer 3: Even without the atmosphere, you won't get a sharp image/shadow because light is not just particles. Instead, light is slightly bent around edges. "This is a problem that my wife does have on her spacecraft." — Matt.

Answer 4: Bec theorizes the optimal time is the empty (i.e. new) Moon, Matt confirms. But the Moon is a bad screen because it's not very reflective: The Earth reflects about 31% of the light hitting it, the Moon only reflects 12%. Matt didn't work out how much brightness you would need, because it's just not possible.

In short: The solution is "no".

A "ding" by Bec

In the past several years, I've taken to running road races. From observation and participating in many races, I've noticed that the winners always wear the shortest shorts, think 5 cm inseam. The people who come last tend to wear shorts that are 30 cm or longer. Is there any possible correlation between running speed and short lengths?

Bec suspects longer shorts get in the way a bit more. She also suspects that full-time runners will invest in shorts for running whereas the people at the end of a marathon just use their multi-purpose shorts, which Matt confirms from personal experience. If wearing shorter shorts made you faster, Usain Bold would run naked.

Matt brings up a similar phenomenon from cycling: People who cycle a lot tend to shave their legs. There doesn't seem to be a practical reason, except to show your dedication to cycling. Bec mentions a barista's top knot as another example. Bec goes on a looong leg hair tangent.

A "ding" from Matt

In problem 014-3, the question came up whether lucky people exist.

Bec asked on Twitter whether listeners think that lucky people exist. The split was roughly 50%/50%. The luckiest person Bec knows, comedian Sarah Bennetto, explains her own luck: She's been entering competitions and won loads of different types of stuff, including a car on a game show. She also mentions a book that talks about the statistics of winning cars.

Matt believes there's no such thing as luck, but there are lucky people. Random processes don't consistently turn out better than expected, but some people make more opportunities or are good at capitalizing on them. Notably, this doesn't mean that past success will lead to more success in the future. For example, Matt suspects Bennetto enters a lot of competitions. He also mentions the Dream Minecraft speedrunning drama.

Matt looked for the book, but couldn't find it and is now asking listeners for help. Bec is prepared to ding the problem when the book is found.

Both of my parents are teachers, and they're teaching from home via Zoom in the current lockdown. One of them has asked every member of the class to bake some biscuits for their maths lesson — measuring, units, etc. My question is: What's the best way for them to share the biscuits with one another?

Originally, this problem was planned for 015, but it had to be pushed back because Matt was too deep in the maths. [Editor's note: biscuits and cookies were previously mentioned in 014-1]

A first approach: Everyone gives them to Bec, and assuming Bec doesn't eat them all, she distributes them to everyone again. For n people, this takes 2n - 3 journeys. After some diversions on cookie parties, Matt has found out that this is not the optimal solution. With the help of some shitty Python code and the Online Encyclopedia of Integer Sequences (OEIS), Matt has found someone else's solution for exactly this problem from 1972, though back then it was called the telephone problem.

Bec recommends a solution where cookies are passed in a big circle, which is apparently the second best solution and takes the same number of journeys as Matt's initial solution. With a bit of extra faff, you can get rid of exactly one more journey, which is the theoretical maximum.

Bec dinged it, Matt will pass on the ding to Raphi, who can then pass it on to their parents.

Tim wants to be efficient with their annual leave and wants to make the most of the time they have off. "Can you please help suggest some interesting ways to elongate the days I have off work in 2021?" They're happy for creative solutions. They were originally thinking of taking the day off when the clocks go back to get a 25 hour day, but that's always on the weekend.

Matt talks about an experiment where people falling were experiencing time differently due to panic. He suggests spending your holiday perpetually falling. Bec suggests skydiving over the international date line. Matt suggests hiring someone to scare Tim occasionally during his holiday. Bec suggests taking her along. Matt shares anecdotes from travelling with Bec, including one about breaking a phone. Bec suggests Tim comes with them to the Edinburgh Fringe and do all their driving and props.

Bec doesn't think she deserves a ding. Awaiting feedback from Tim. Matt will add a dropdown to the Problem Posing Page from episode 015 (news) where you can select "solution".

How many Bec Hills could fit in Bexhill? [Editor's note: Bexhill is a town, and not in fact a hill.]

Bec has never been to Bexhill. Matt frequents Matthew Parker Street, and has even been to Bexhill, just after they broke the world record for number of mermaids in a single area. In 2012, Bexhill was found to have the highest amount of centenarians in the UK. In October 2021, the East Sussex Astronomical Society will be hosting Lucie Green (Matt's wife) as their speaker.

Bec has scrawled all her calculations on her hand, which are slightly smudged. Bexhill is 32.31 km². Instead of measuring her own diameter (see problem 011-2), she measured her rectangular dimensions, which are 29 cm by 45 cm. The answer: 247'586'206 Bec Hills fit in Bexhill.

But how many actual people called Bec Hill can fit in Bexhill? With the help of some websites, she estimated that there are 81 Bec Hills in the world. However, that's only those born as "Bec", not "Rebecca". Including Rebeccas, there should be 23'757 Bec Hills in the world. Bexhill currently has about twice as many residents, so the answer is: Every Bec Hill could live in Bexhill.

A "That's 100% a ding, well done" from Matt

If you got every animal, which species would form the longest queue when all individuals of that species would be queuing up.

Matt asks Bec for her intuition. She suggests rats or cockroaches. Producer Jon guesses cows, which are big and there are a lot. There's a also lots of chickens. Lucie guessed worms.

Matt could not find a good database for animal species population sizes nor animal sizes, so he had to do the calculations by hand. Humans in a queue lying down would be 13 million km long, but standing up it would only be 2.2 million km long. If humans can't lie down, cows are about 3.6 million km long, and chickens are about 11.6 million km long. Ants across species would be 54.7 billion km long, which makes about 4 million km if you assume they're distributed into species randomly. There is no clear answer. Biology is a mess.

Excluding bacteria and worms, the answer is humans (if we're allowed to lie down), otherwise chickens.

A "I think that is worthy of a ding" by Bec

An "absolute ding" by Matt, and a "ding" by Bec

In an upcoming election, I want to vote for a novelty candidate, not just because I think it would be funny, but also because I think they would be good if they won. But I'm also aware that novelty candidates rarely ever win, and I'm worried that voting for them could be an irresponsible use of my vote. What should I do?

Matt is an amateur voting system nerd. The system used in the UK is first-past-the post, where the candidate with the most votes wins. Australia has (compulsory, with democracy sausages) ranked-choice voting, where you rank candidates instead of voting for a single candidate. As candidates drop out, your vote rolls down your list to the next candidate. For completeness, there is also is approval voting, where you mark all candidates that you would approve of winning, and the candidate with the most approvals wins. Matt mentions Arrow's impossibility theorem, which states that no voting system can be perfect. Nonetheless, some voting systems are better in practice.

In conclusion, first-past-the-post (and approval voting) encourage strategic voting. If it's going to be close, maybe don't vote instead of the novelty candidate. Bec reveals she was the novelty candidate once. She also mentions Antanas Mockus, who was a mayor in Columbia with over-the-top but working initiatives.

Finally, the big reveal: Bec was considering voting for Count Binface, who appears live on the podcast. He notes the London mayor election does not use a first-past-the-post system. Because many seats in the UK's system are safe, novelty candidates like Boris Johnson and Donald Trump do arise from time to time.

How do I explain Eurovision to Americans?

It's X-Factor, but where the contestants are countries, and crossed with a circus.

A "ding, that works" by Matt

What's something I can say or do to make a good impression when meeting people for the first time?

Bec briefly did door-to-door sales. One of her co-workers, now-comedian Chris Knight, would have a pack of cards. As people opened their door, he'd hold up a card and ask "Is this your card?". Matt holds up a card and asks Bec the same question, though sadly it was not Bec's card.

Bec also suggests to use people's names more often, both to remember it better and because people like hearing their own name. Matt suggests asking people about themselves. Bec suggests body language mirroring, or matching the energy. She also suggests showing up on time. Though if you're in a position of power, be very slightly late.

If the location name "Wyoming" was a name (i.e. running, parachuting, kerploding), what would it mean?

It's the verb of wyome. Matt thought it was to question why you're meditating (why omm?). Bec suggests it's being unsure when asking questions (why — umm...). Urban dictionary suggests "wondering" or "wandering", or "to flap about like a worm". Matt googles that it comes from a word meaning "at the big river flat", so "wyoming" means arriving at such a river flat.

A "ding" by Bec

How many podcasts should I subscribe to?

There's no "too many", subscribe to as many as you want to listen to. Bec listens to lots of podcasts. She suggests "Office Ladies", "Swindled".

A "ding" by Matt

How many people have successfully faked their own death?

Bec doesn't know the answer, but she recommends the true crime podcast "Casefile", who are releasing a new series "Pseudocide" about people who fake their own deaths. Matt reckons you might be able to estimate it if you have different methods for measuring population size, e.g. sewage. Bec notes that if somebody is claiming to be dead, they're lying. But after a certain amount of time, any fake death becomes a real death.

An "I think your advice to go listen to a podcast about it is the best ding we're going to give it" by Matt.

A very special, limited edition ding.

Six months ago, I found a hamster in my apartment. None of the neighbours claimed him [though the problem poser does not know if it's really a him]. I don't know if it's really a hamster or a mouse with its tail cut off, I don't know how old he is, but most importantly, I still have no idea where he came from. I live in Pakistan, we don't have hamsters. WHERE DID HE COME FROM??

Bec got a photo and video of Hammie and she can confirm that it is indeed a (short haired Syrian) hamster. She has experience with hamsters, in particular a Russian dwarf hamster called Pudding first mentioned in episode 012 (news). It seems he may have testicles. While you can cut a hamster in half and count the rings, it will probably not help determine its age. Hamsters tend to live two years, so Hammie is probably not older than that.

Hamsters are not illegal in Pakistan (unlike Australia) and there are hamster breeders in the problem poser's town, so it's likely someone's pet. Hammie didn't seem to be in best shape, so it may have been a neighbour getting rid of their pet. On the other hand, hamsters can run up to 9 km a night, as mentioned in 012 (news), so maybe Hammie came from a neighbourhood a few km away. Hamsters are also very good climbers and used to tight spaces, which explains how Hammie made their way into the apartment.

If you find a hamster, you should know this: Hamsters need a lot of space (because they like to run), and ideally not something tall made of bars (else they might slip and break their back). A big multipurpose plastic box (with holes and mesh for ventilation) or an IKEA Detolf display cabinet laid on its side make for good cages.

"There's some good hamster porn." — Bec

A full ding by the problem poser

If humans were able to grow trunks and leaves to use photosynthesis to harness energy from the sun, how big would our human leafy crown have to be to sustain our daily energy expenditure?

Matt needs about 2'500 kcal per day, which is 10'460'000 J per day, or roughly 121 W. Plants have a worse efficiency than solar panels and produce around 8.1 W per m³. This means Matt would need around 15 m² of leaves; roughly a square twice as big as his height. If you exert yourself carrying around a big trunk, you might easily need twice as much energy. Bec notes that this is why trees don't walk around. Matt notes the similarity to the rocket equation.

A "ding" by Bec

An "A ding to Bec" by Matt

I'm wondering whether the planet is warming because of the increased relative proportion of carbon dioxide in the atmosphere, or the absolute amount. If it's the proportion, then could we alleviate the problem (theoretically at least) by putting loads more nitrogen and oxygen into the atmosphere?

We usually talk about it in ppm (parts per million), which is relative. Matt compares CO₂ to the bouncer of a club who lets high-frequency radiation through but not low-frequency radiation. The same amount of bouncers in a hallway that's twice as long are still as likely to catch you as before. However, the Earth is a sphere, so diluting would actually have a slightly positive effect. This apparently corresponds to a club where the bouncers stop you from leaving because you're too sober.

While it may technically work, you'd need about 85 times the atmosphere to reduce the greenhouse effect to pre-industrial levels. This would increase the atmospheric pressure by 85 times, while the human record (some deep sea diver) is around 75 times. If we manage to live like this, global warming is solved!

Bec is not giving it a ding until they hear back from any deep sea divers.

Andrew thought of this because in episode 018 (news), Bec mentioned she likes falling over like a plank. Andrew however has a medical condition which causes them to pass out randomly and unexpectedly. This goes along with a condition that means they dislocate their joints when doing this rather than breaking them. How would you reduce injury and/or make it the most funny? Since life is limited, less pain and more laughing is always good.

Bec is not giving pain relief or medical advice. She mentions Rowan Atkinson's "Funny Business", which Matt has also seen. Matt warns that standup comedians talking about comedy is a very dry subject.

Context: Something serious can be made funny if you know the consequences are not serious. Bec proposes Andrew should either only frequent soft places (bouncy castles, trampolines, pillow factories), or Andrew could wear something soft and protective.

Incongruenty: Pattern breaking, related to the rule of three. Anything can be funny if it appears somewhere unexpected (horse in an office), looks unexpected (the horse is tiny), or behaves unexpected (the horse is answering the phone). Andrew passing out unexpectedly is already funny by that measure.

Superiority/ranking: Andrew should look like they have a lot of money or power, i.e. should dress like the Monopoly man.

Public shaming: Something happening to you is funnier if you look like you deserve it (e.g. running over an ice lake). Andrew should be a jerk all the time, steal candy, down low too slow, ...

Relief: Building up tension and then releasing it, usually in verbal comedy and story telling. This would require timing on Andrew's part, which is not applicable.

Psychological distance: If you're distant (e.g. they're on TV, you don't like them), you might find it funnier.

Matt also suggests a T-Shirt with "It's okay, I thought it was funny as well" on the back. Bec warns of an "explosion at a clown factory", where too much funny factors make something unfunny.

Bec's conclusion: Andrew needs to become a sports mascot. It's padded and cartoony. Sports games have a lot of tension, relieved by mascots. They also are priviledged, getting to interact with the players. You're physically distant and thus psychologically distant. This is both career and life advice.

Matt tells an anecdote where he wore a galah mascot costume and ran into windows. He entered the video into Australia's Funniest Home Videos and got 500 bucks for it. Bec hopes Matt or a listener will find the footage.

Awaiting ding from Andrew.

Have you ever felt like your dings were missing something? What's the closest that the human vocal apparatus can get to mimicking the "ding" of an actual bell?

Bec starts by explaining the basics of sound, frequency, volume, partials, and harmonics/inharmonics with the analogy of throwing differently sized balls from a roof. She demonstrates overtones by singing, after which she plays a clip by singer Anna-Maria Hefele for comparison.

Bec brings on Beardyman (Jay Foreman's brother), who explains the difference between the human vocal tract and a ringing metal object. Some resonances will be canceling each other out and some reinforcing each other, as previously described in 005-1. Beardyman also explains the basics of attack, sustain, and release. He then creates a bell-like noise from his voice with the help of a frequency shifter. Apparently, the lyrebird is also capable of introducing inharmonics because it kind of has two throats.

The human voice might be able to mimic a bell if you find a way to produce inharmonics and have a quick attack and long release. If any listener is capable of this, they should get in contact.

"Inharmonics is just harmonics you don't like." — Matt

A Beardyman ding

Now that the weather is getting better, I need to use sunscreen, otherwise I get burnt. But I don't want to use too much sunscreen, otherwise I don't get a tan at all and am therefore more susceptible to sunburn. How do I optimize my usage of sunscreen?

To an Australian, a healthy tan is like a relaxing concussion. You get burnt by UV rays from the sun, which are the high-frequency parts of the spectrum. The warmth you feel is the low-frequency, infrared range. The most dangerous radiation, UV-C, is blocked by the ozone layer. UV-B is only partially stopped, and sunscreens mostly block this part. The bulk of UV radiation is UV-A, which is not as dangerous but still not perfect.

There is a technical difference between a sunblock and a sunscreen: A sunblock deflects the radiation, while a sunscreen absorbs the radiation (and breaks down in the process, which is why you have to reapply it). The factor is which fraction of light is let through: Factor 30 means ¹/₃₀ of the light makes it through. Factors are determined by intentionally sunburning a poor volunteer.

The results from the survey are in. Matt wanted to see if countries name their sun protection positive or negative depending on the sun severity. Australia and the USA are pretty sun-negative, while the UK is a bit more sun-positive. There's not a big correlation with age.

Having a tan is somewhere in the region of SPF 2 to 4. Putting on less sunscreen because you have a tan is a dangerous game to play. No UV exposure is safe exposure. Always put on your sunscreen.

A "ding" by Bec and a Beardyman ding

A "DING" by Andrew

A "full ding" by Bec and a Beardyman ding

How to avoid burning out with writing and ways to keep it fun and interesting

Bec and Matt talk about the books they're writing. When Bec was writing episodes for children's shows, they were so short she didn't get bored. Writing a rough first draft is quick, but honing it takes a long time. Don't worry about making it perfect on the first go, that's just wasted energy. You have to be okay with making a bad thing, but you do get to fix it later.

Sometimes Bec wears differently-colored 3D glasses. Sometimes she switches up the font, e.g. Comic Sans (all of Matt's books have been written in Verdana). Bec has bought an E-Ink tablet and a clacky bluetooth keyboard to kind of emulate a type writer, which makes writing more fun. Matt has some fidget toys nearby and he likes throwing things in the air and leaning very far back in the chair.

Don't write for more than three or four hours at a time, otherwise you'll not be very productive. Matt recommends to stop writing when you're excited, and to write down a few ideas. This way, you'll have a good starting point the next day. Matt uses post-it notes on his wall to structure his books.

Awaiting ding from James.

It's easy to look at a star that's light years away, but I was wondering where on Earth you can look the furthest away at something that is also on Earth. As in: What's the longest line between two points on Earth that doesn't go through the Earth, and where are those two points?

Matt first wanted to know what's the furthest thing away that you can see with your bare eyes: It's the Andromeda galaxy. From time to time, supernovae further away are also visible. Bec wants to coin the term "blip" for a supernova you can see with the naked eye.

The taller you are, the further away the horizon is. Matt recounts a related Lucie anecdote. Matt has a spreadsheet to calculate personal horizons. If you built a tower up the the line where space starts, you could see just over 2000 km in every direction. From the tallest existing building, the Burj Khalifa, you could see 103 km, and there is a direct line of sight to the top of the tallest building in Abu Dhabi. Bec asks about two mountains; Matt is open for suggestions.

Waiting for a reply from Lois.

When eating cereal, what is the milk? Sauce, broth, jus, or something else?

Bec did some research: It's milk! It's not broth, jus, gravy, soup, or stock, because those all involve boiling the ingredients to get the flavour out of them. A sauce is made out of a variety of ingredients, which milk is not. It's a bit like cold-brew tea where you eat the tea, or like custard. If you added some stuff to the milk before pouring it, it could be a sauce.

A simultaneous Bec "ding" and Beardyman ding

If you rolled up graphene into a roll the size of a toilet paper roll, how long would it be?

Graphene is a one atom thick material that's very strong for its mass. According to a paper, an accurate thickness measurement is difficult because measuring it squashes it, but it's rougly 0.5 nm high. Approximating the Achimedean spiral using concentric circles, Matt arrives at a length of 20'000 km, which is halfway around the Earth.

"Give me two rolls of graphene toilet paper and a place to stand, and I will TP the world." — Matt, paraphrasing Achimedes

A tentative "ding" from Bec

My brother told me that every time he reads a paper book, he wonders how much the book would weigh without any ink. If you had a totally useless representation of a book, how many pages could you save by just printing the ink without any gaps?

Bec's Horror Heights book is being released on the date of this episode, 2021-09-30, and she got a tour of the factory. She nerds out about the printing process. Bec asked Beth and Ollie from Clays Printing (who printed her book), who estimated 11.2 g per book. Each book is 157.3g, which makes 146.1g per inkless book. The ink is about 7.12% of the mass.

Matt wrote a bit of Python code to count pixels of ink in Bec's book. After some fun stats, he reveals you'd only need 24.22 pages full of ink to equal the 176 actual pages. Matt uses this opportunity to talk about the difference between the mean and median.

A "solid ding, margin to margin" from Bec and Matt

A solid ding from Bec, which turns out to be a Beardyman ding

A Beardyman ding as a meta-ding

What is the largest single hole relative to the size of the pumpkin one can carve out of a pumpkin without the pumpkin collapsing? How should one cut said hole?

You can cut a hole in the pumpkin that is bigger than the pumpkin, which does not involve deforming the pumpkin. This is related to the Prince Rupert's cube, where you cut a hole through a cube that you can fit the cube through. Matt verified this fact in a practical experiment with two same-sized pumpkins, one of which he cut a hole into. The other pumpkin then fits through the hole. He used the smallest pointiest knife, and he never cut towards himself because it would slip very easily.

Bec decides to wait for a ding from Eric, even though she personaly considers the problem dinged. Bec wonders at which point it ceases to be a hole in a pumpkin, like the point where a bowl turns into a plate.

How do I stop the ghosts in my place from rattling all the doors during the night when I'm trying to sleep and I have to get up at 4am for the early shift at work? I've pleaded with them, had a stern talking to them, but they won't listen.

Bec suggests the ghosts might not be the problem, and instead Greg should fix the rattling doors. She quizzes Matt on the names of door parts, then explains them in detail.

One of the common causes for door rattling is that the strike plate is too big, which causes the latch to move around and rattle. You can also use weather stripping on the door jamb, which not only stops rattling but also minimizes sound leakage. You could wedge the door, or use plastic strip courtains instead of doors.

A door fun fact from Bec: January is named after Janus, who is the god of doors.

In case the ghosts are the problem and not the doors, Bec looked up what to do about noisy flat mates. Don't confront them directly but talk calmly. Be ready to accept compromises. Maybe escalate along official channels if this didn't help. To get rid of the ghosts, try burning sage (to a CD-ROM, ghosts hate pirates). Sound reiki might also work, both for spiritual people and for geology nerds.

"Finding common ground: Rocks" — Matt

If everyone in the world gave me one in their local currency, how much money would I have in Euros?

Some countries accept multiple currencies, in which case Matt is using the most local currency with an ISO abbreviation. He then wrote some code to google the exchange rates. The worst case is Indonesia, which is the 4th most populated country with one of the worst value-per-unit rates. The best exchange rates are Kuwait, Bahrain, Oman.

The overall result is 1'229'461'715 €. The average person would give you 0.158 €.

A "ding" and a "ka-ching" from Bec

Building on 017-1: How many Beck's fit in Bec Hill (both by consumption and theoretical total volume)?

By consumption: Bec and Matt drank as many Beck's as they could and recorded the process. Some of the beers they drank were non-alcoholic ones. Bec complains that Matt was a terrible control. Once you use the bathroom, the experiment stops. In the end, both drank 6 bottles, which comprises a third of what they bought.

By volume: Bec has looked at X-Rays, but the max amount of bottles were one. She also asked two sword swallowers, Snookie Mono and Snake Fervor, about this. Both said "don't swallow bottles, you will die". Conclusion: Don't insert any bottles in any way, it's not safe. She also reached out to two doctors, Adam Kay and Doctor Xand, who said that skin is very stretchy and suggested surgically implanting the bottles.

To measure her volume, Bec had a bath at Matt's house. Matt then calculated the volume of the displaced water, which was 56.5l. In beer, that's the content of 205.5 bottles.

A "full ding from me" from Eric

How fast could a team of penguins complete a 4x100 relay race? Could they field a competitive (or uncompetitive) olympic team for Antarctica in 2024?

Matt spoke to a penguin expert (a human) on the ship, and he saw a lot of penguins, which he thinks are a stupid animal. On land, penguins are slow because they have no land-based predators. The fastest penguin is the

Gentoo (which Matt hears as "Gen. 2"), which goes 35.4 kmh under water. It would do a 100 m sprint in 10.17 s. Obviously, they would use fish batons. The entire race would take 40.67 s, which is better than the current women's record (on land) but worse than the current men's record (on land). They'd be a lot faster than the human swimming records.

On land, penguins can waddle and slide on their stomachs. Matt took a video of two penguins doing just that, and estimated their speeds. The waddling penguin went 0.7 m/s while the sliding penguin went 1.75 m/s. The waddling race would take 9 minutes 31 seconds, while the sliding race would take 5 minutes 26 seconds.

A simultaneous Bec "ding" and Beardyman ding

How can I fix my sleeping schedule? For the past year or so, it seems to have gotten worse and worse. I am a grad student and I have to work a lot, often into the night. But then I wake up very late in the day. I feel guilty about sleeping and stay up even later the next day, and sleep in even later. It doesn't matter how many alarms I set, I can't seem to wake up at a decent time. I have even tried multiple times to stay up all night, hoping to reset to a normal bedtime the next day, but that does not stick.

PS: As part of this endeavour, I've tried to stop looking at my phone before bed because I always hear that the changing lights stimulate your brain and prevent you from sleeping. No scrolling through social media or watching videos. Your podcast has been something relaxing that I can listen to but not watch while getting ready for bed.

Bec builds an analogy for the circadian rhythm based on a smart home with a control hub in the kitchen. There's multiple circadian rhythms, all connected to each other, and they can be disrupted.

Bec thinks Sleepy should let their body adjust to their current sleep cycle before trying to set a new sleep cycle. It might not be the schedule they want but it would be a schedule. They should then stay in that schedule for a few days. Circadian rhythms don't like hard resets (which is also why you have jet lag). As a rule of thumb, you should calculate one 24h cycle for one hour of time difference.

More tips: As soon as you wake up, get some sun light on you. Bec uses an alarm clock that slowly becomes brighter, which is great. No caffeine within 5 hours of your bedtime. Exercise helps a lot (Bec speaks from experience). Holidays are a good time to start new habits because your body is already in disarray a bit. Sleep in a cool room. Set your alarm earlier by small increments (e.g. 30 minutes).

Finally, there's A people (early birds) and B people (night owls), which is probably based on genetics and not possible to change. Different countries have different sleeping habits. Greece goes to bed the latest. Matt sleeps like a spanish woman.

Awaiting reply from Sleepy.

I love the podcast. It has been keeping me sane whilst I've been going through radiotherapy for a brain tumor. I've now finished my therapy and received a mesh mask of my face/head that was needed to hold my head still throughout my radiotherapy sessions. What should I do with the mask? My wife is an artist and I've thought about asking her to paint it like a popular arachnid-based superhero, but I think there could be a more creative answer out there.

Bec, who has a copy of her own head — 027 (news) — notes the difference between a mask and a head. People commonly do cool stuff with their radiotherapy masks.

Bec's ideas: Wastepaper basket, novelty basketball hoop, use it for fencing, pop it into a hot bath and remold it, ice sculpting, make a massive jelly/jello (and serve it in the blounge room), papier-mâché it and make it look like somebody is pressing their face through the wall, a planter, place a light bulb behind it, use it to paint your own face through the holes, use it to stamp makeup onto your face. Also, Chris should ask his wife, the artist, for ideas.

What UK postcode has the highest Scrabble value? Does this change if you include the actual digits in the postcode?

Matt tells some postcode related anecdotes. Compared to other countries, UK postcodes are very detailed. They include both letters and numbers. Technically, there are enough postcodes that you could have a postcode for your cupboard.

Matt downloaded all UK postcodes and wrote some Python code to compute their Scrabble values. Of the postcodes with the maximum value of 35 points (ignoring digits), WC1X 9QZ in London is Matt's favourite. If you include digits individually, BN99 8ZZ and EX39 9ZZ are tied for 50 points. If you combine the digits, BN99 8ZZ wins with 131 points. Using 1337-speak (i.e. swapping numbers into their corresponding characters), EH22 2QQ and EH22 2QZ are tied on 55 points.

A "d1ng" from Matt

The longest ding the hosts have ever seen

Assuming the signal was strong enough, what would happen if you tried to use a GPS satnav on the moon?

GPS satellites constantly yell the time into space. The signal travels with light speed, so you can calculate your distance to the satellite based on the delay. In n dimensions, you need at least n+1 satellites. A GPS receiver needs to know its location in 4D spacetime, so it needs 5 satellites (though 4 satellites can suffice if you assume you're on Earth). If you've got enough satellites, in theory you can find your position anywhere in space.

However, your satnav might still not work on the moon because the satellites are all very close together from your perspective, so your position estimate is very inaccurate. Matt suspects it wouldn't even reliably place you on the moon.

However, your satnav would refuse to work anyways. To avoid it being used in missiles, it will stop working if it moves faster than 1000 knots (1852 km/h) or if it is more than 18 km above sea level. Some manufacturers see this constraint as a logical "and" and some as a logical "or" though. If you get a manufacturer that views it as "and", in theory you would be just 100 km/h inside the speed limit relative to the surface of the Earth, but due to the inaccuracies, it will probably not work anyways.

A combination Bec and Beardyman ding

The poser enjoys a podcast with a running joke that involves one host asking the other "Is this your card?". They've lost track of why it's a running joke, how it started, why it's funny. They're too afraid to ask the hosts to explain the joke (at least directly) because they think it might ruin it.

Bec can't remember, neither can Matt. Bec argues that it is not a joke, and that Matt is actually trying to find Bec's card. [Editor's note: It originates from 018-3.] They request listener assistance to solve this problem.

Awakey considers it solved. A combination Matt and Beardyman ding.

While they were grocery shopping, they noticed that there were some words that may freely be used on products whereas others can only be used on specific ones. In Germany, "premium" can be used freely whereas the word for "chocolate" can only be used on specific products. They'd like to know more examples which are or are not reserved on food products.

Bec spoke to a lot of people to solve this problem. She even took a course and got a certificate. All of her research was limited to the UK. Mislabeling your groceries is a food crime.

Bec explains a bunch of rules and examples, including chocolate and milk vs oat milk. There were apparently court cases against Froot Loops and Cap'n Crunch Crunch Berries for suggesting that they contain fruit. Quite a lot of super markets got in trouble because of their in-house brand names. Bec explains the differences between fruit juice and nectar. Bec explains the difference between natural mineral water, spring water, and plain bottled water. Jam apparently has a lot of rules. Finally, barn eggs only require 15 cm perch space per hen and only 1 m² of floor space per 9 chickens.

A preemptive free-range ding from Matt (with Beardyman undertones)

How much of a public servant's salary is paid by their own taxes?

Matt, having been a teacher, uses teaching salaries for his calculations. Roughly 0.0000006% of the UK government spending came from a single teacher's pay. Over a year, 0.02 pence of the teacher's salary comes from their own salary. Almost exactly, all the tax paid by all parents from a teacher's class is one penny of your annual salary.

0.02 of Bec's ding

So I was driving in my car today and had the following thought: What are the odds of having the same child twice? Not twins! Giving birth to a child, getting pregnant, then having the exact same child again by the same parents. It's infinitesimal, but how much compared to other infinitesimally unlikely occurrences?

A human cell has 23 pairs of chromosomes, for redundancy. When the body makes a reproductive cell (sperm/egg), only one of each pair is chosen. This makes for 2²³ = 8'388'608 possible options per parent, or 70 trillion possible children. In other words, the second child has a one-in-70-trillion chance of being the same as the first.

However, biology is a lot more complicated and there's actually a lot more combinations. Including some of those effects, there's 3 * 10¹⁶⁶ possible options for a reproductive cell starting with an XX configuration and 2*^0¹⁶⁰ starting with an XY configuration. The number of combinations for a single child has over 300 digits.

The probability of having a child and then another identical child is the equivalent of picking a single proton from the entire observable universe, mixing it back in, and randomly picking it again, four times in total. In short, it's not going to happen. It's slimpossible (there's an infinitesimally small chance, but it's practically impossible).

A "from my angle, I'm giving it a ding" from Bec (combined with a Beardyman ding)

Are there more wheels or doors in the world?

Both Matt and Bec came to the conclusion "doors".

A "ding" by Bec and a "ding ding ding" by Matt

APS is the first podcast Eva listens to regularly, and they really like the format. They want to listen to more, however they don't know how to find more good ones. Thus, they ask for recommendations.

Bec recommends A Podcast Of Unnecessary Detail (featuring Matt), Science Vs, Mathematical Objects, Reply All, Darknet Diaries, The Dream Factory.

The Dream Factory talks about hypothetical movies with pun titles. Matt spontaneously comes up with "Fast & Spurious", which Bec promises to send in to the podcast.

A combined Matt and Beardyman ding

An un-gnid-able ding by Dennis, combined with a Beardyman ding

Why are aspect ratios all whack? [The poser rambles on for a while.]

It's almost like different people making different things make different decisions. Bec asks Tom Salinsky onto the podcast to explain why movie aspect ratios are whack. Tom explains that things used to be made of stuff. Originally, things were a mess, but when sound came along, frame rates and aspect ratios were standardized by the Academy to roughly 4:3. Once TV came along, movies became wider. Showing movies on devices with different aspect ratio comes with a whole host of issues. Thanks to Dr. Kerns H. Powers, TVs (and other devices) now have a 16:9 aspect ratio. However, nowadays 2:1 is becoming more popular. Matt complains that there are two different 4K resolutions. Some films switch between different aspect ratios, which Matt is always excited about.

A "I think this — at least from where I'm standing — you've just given us a good ol' ding." from Bec, combined with a Beardyman ding

I got a missed call from a mobile number earlier today, but when I rang it up, I was informed the number had been disconnected. This got me thinking about how many mobile phone numbers there are. How do the Australian numbers compare to the UK and the US, and would we ever run out?

Matt tells a related anecdote about his teacher days. There are 100'000'000 possible mobile phone numbers in Australia, or roughly four per person. In the UK, there's 1'000'000'000 numbers, or roughly 15 per person. In the US and Canada combined, there's 6'400'000'000 numbers, or roughly 17 per person. Matt thinks there should just be a few more digits and there should be a check digit.

Kids nowadays don't remember their parent's phone numbers, Bec doesn't know her husband's. Matt knows three phone numbers by heart: His own, his wife's, and some friend's parent's house from the 90s. Matt tells another anecdote related to recycled phone numbers and the UFC.

How many molehills would you need to make a mountain out of them?

Matt went and found a molehill (frustrum-shaped), which he then measured. A mountain needs to be at least 1000 ft (304.8 m) to be considered a mountain and not a hill. To compute the volume, Matt takes into accounnt the angle of repose, i.e. how the dirt slumps. Bec notes the problem's similarity to problem 011-2. In total, you need 3'060'370'873 molehills to make a mountain.

As a Hill, Bec approves and gives this problem a ding.

How can one make friends after adulthood? It's weird not being able to just hang out and talk about stuff. How can one make new friends and not just adult acquaintances?

Bec doesn't have an acquaintance setting, she is always in friend mode. She suggests just forcing yourself on people (not physically though). If you go in with the expectation that you will be friends, most people won't resist it. She also suggests repeating someone's name when talking to someone, to remember it better. Bec made a lot more friends when she started putting herself out there and doing things on her own (e.g. signing up for clubs and sports activities). Bec suggests improv clubs. You also need to be proactive and make plans, things won't happen on their own. Matt's strategy is stealing friends from other friends, though this also requires being proactive. Bec recommends common interest groups for things you're passionate about.

Bec tries to start #friendding to share friend advice and stories.

Can one produce less smelling or even well smelling farts by eating or drinking a certain food?

Bec is uniquely qualified because she has IBS and the sense of humour to match. High protein foods cause smelly farts, but that was not enough for Bec. She contacted experts Dr. CK Yao and Dr. Jessica Biesiekierski, the latter of which recorded a voice message with lots of detail and food suggestions for both nicer and worse smells.

Bec has also found a french fart pill (Pilule Pet) which is meant to make your farts smell like roses. Of course Bec ordered some. Jessica is sceptical, but suggested charcoal fart pads. The fart pill ingredients list was turned into a parody song by Gareth Turkington.

A "ding" by Matt and a raspberry by Bec, even with the pill test results still pending

When does a computer become a supercomputer, and do publicly purchaseable personal computers surpass the capabilities of the first/early supercomputers? If so, how much would it cost?

A supercomputer is just a very powerful normal computer. Actually, supercomputers are a lot of processors joined together for one or more big tasks. Matt got to walk around inside two supercomputers.

Supercomputers are measured in floating point operations per second (FLOPS). The iPhone 12 can do roughly 10¹⁰ FLOPS, an M1 Mac's GPU has 10¹² FLOPS, while current top supercomputers can do 10¹⁷ FLOPS. In the past, Moore's law predicts computers become twice as powerful every two years (though it has to be taken with a grain of salt), so in 50 years, a phone should have the equivalent power to a modern-day supercomputer. Looking into the past, the old Cray supercomputers were doing around 10⁸ FLOPS, or roughly 1% of a modern-day iPhone.

A "dinglet" by Bec