Episode 006 = Squaring Shirts and Testing Toasters

2020-04-30
00:36:47

News: Lock-in updates
00:01:11–00:02:41

Bec's coping quite well, but her fitbit keeps telling her off for not walking enough. Following government advice, Matt and Lucie have now opened a pub in their backyard.

Problem 006-1 = The £5K T shirt
00:02:44–00:17:28

Problem poser: Bec
Problem solver: Matt

Problem statement

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?

Solution attempt

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.

Problem 006-2 = How much energy do dried clothes have?
00:17:32–00:22:55

Problem poser: @hgoldstein95, on Twitter
Problem solver: Matt

Problem statement

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

Solution attempt

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.

Ding

A "ding" by Bec

Problem 006-3 = Limmy's toaster conundrums
00:22:57–00:32:35

Problem poser: Limmy, on his show
Problem solver: Bec

Problem statement

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?

Solution attempt

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."

Update for problem 006-1
00:32:38–00:34:00

The code is done! 3cm by 3cm squares, one 11 by 20 block and one 14 by 20 block (one on the front and one on the back). Bec will take the average of Matt's and Mike's solutions and do 3.5 cm by 3.5 cm squares.

Update for problem 005-1
00:34:09–00:34:56

@McKGerald on twitter thinks Matt is right about the surround sound encoding: Bec sounded like she was behind them. Bec's mate Ron from Northern Ireland reckons he can fix Bec's audio file.

Update for problem 005-2
00:34:57–00:35:18

Bec and Matt received a tweet containing only a solitary ding.

Ding

By Bridget B