001 = Sizing Shoes and Selling Organs

**Sizing Shoes and Selling Organs** is the first episode of A Problem Squared.

* What's the deal with shoe sizes?
* Buy my body!
* Re-refridgeration.
* Nice knick-knacks for nieces.

Bec Hill: (Link)

Matt Parker: (Link)

#### What's the Deal with Shoe Sizes?

The first ever problem posed to A Problem Squared was posed by Bec to Matt relating to shoe sizes. Bec noted that the sizes never make any sense no matter where she got them from, and that the sizes don't go up in an orderly manner (e.g. the difference between a 6 and a 7 isn't the same as a 7 to an 8).

Matt started by stating that UK and US (men's and women's) shoe sizes are on the same scale, with a difference of 1 between them. For example, if someone wore a UK size 10, it would be a US (men's) 11 and a US (women's) 12 respectively.

Shoes in the UK are all on the same linear scale, regardless of if they're adult or kid-sized. Kid shoes use a scale from 1-13, where a UK kid's size 13 is equivalent to a UK adult size 0. They are pegged to the foot (scale), where a UK adult size 12 is 12 inches long (304.8mm) and each size is different by one barleycorn (equivalent to 1/3 of an inch or 8.47mm). UK shoes are not made using a real foot, but a model one called a last. According to Matt's understanding, the shoe made will offset by being 1/5 of an inch (5.08mm) than the ideal size.

Shoe sizes in Europe are also on a linear scale, and each size difference is 2/3cm (around 0.26 inches), with an offset of 1.5cm (around 0.59 inches). Since the offset is larger than the difference, in theory, a European size 1 would fit a foot size of -5/6cm (around -0.33 inches).

Matt's solution to confusing shoe sizes would be to ignore the old model feet used for shoe sizes, measure the size of the foot and round it off to the nearest 1/2cm, and to also consider foot widths as well as lengths (like jean measurements in waist and length). This system was already made before (disappointingly), and it's called Mondopoint sizing and it always rounds down to the nearest 1/2cm.

#### Buy my body!

A problem sent in by a soon-to-be listener named Mikey on Bec's Twitter was "What is the most number of (someone's) organs they could sell at the highest price to make the most profit without dying?" This question was tackled by Bec, who started researching which organs you could live without. According to a BBC news article[*citation needed*], humans can live without one lung, one kidney, the spleen, appendix, gall bladder, adenoids, tonsils, some lymph nodes, fibular bones, up to 6 ribs, uterus, ovaries, breasts, testicles, and prostate.

In addition, with medical assistance (like a dialysis machine), one can also sell their stomach, part of the colon, pancreas, salivary glands, thyroid, bladder, the other kidney, eyes, ears, nose, limbs, larynx, tongue, lower spine, rectum, skull, heart and the other lung.

While it strongly advised that listeners do not attempt to perform this sale (for obvious reasons), Bec also mentioned that losing all parts at once could risk making someone go into hypovolemic shock, and even getting them removed one at a time would compromise the immune system and risk infections.

There are several ways to sell the organs, like the black market (which is illegal), as well as organ brokers, who take a cut of the fee for themselves. While the selling price for a kidney might be £105,000 (US$130,000), after the cuts from the broker, and the cost of surgery, it would be around £800-8000 (US$1000-10,000) of profit, depending on how much the broker takes.

Bec put all the values into a spreadsheet, and calculated that a male (given he give up his two testicles) would make up to £361,424.30 without medical assistance, and up to around £900,000 with medical assistance to keep him alive. She also explored different ways to passively make income with your body, such as selling blood for transplants, hair for wigs and semen and eggs for infertility.

Bec also mentioned about her "tooth fairy" project, in which she is buying teeth for £2 each, £5 for wisdom teeth. She said she doesn't know what she'll be doing with them yet, but to contact her if you've got teeth to sell.

#### Re-refridgeration

A problem sent in by PRL (@UsrBinPRL) on Bec's Twitter asked, "Given that the general cost of a fridge is electricity, and that fridges become more energy efficient while electricity gets more expensive, how often should one replace their fridge?" This question was tackled by Matt, who started researching how energy efficient fridges have been getting. In the 1970s, fridges used around 2000 kWh/year (roughly 860 cal.) and they went down to around 750kWh/year in the 90s, 500kWh/year in the 2000s, and not more than 250kWh/year at the time of recording (2019).

He then looked up the wholesale electricity costs over the last decade, from 2010 to August 2019, and while prices go up and down, he averaged, based on the 12-month periods, he figured that electricity got around 10% more expensive over the last decade (even though they went down for the first 6-7 years).

He then searched a website for fridges, and took their costs, volumes for fridges and freezers, and kWh/year. Switching from a fridge from the 90s to a 250kWh/yr one, one would get their money's worth in 3.5 years. From a 2000s fridge to a 250kWh/year one, it would take 7 years. It would still be cheaper to get rid of the old fridge and buy the new fridge, getting one's money's worth in 4-7 years.

In environmental terms, Matt admitted that he never checked the impact of getting rid of an old fridge, but reckoned it would be better if you replaced a 5-year-old or older fridge for a new one.

When asked to clarify on the rate, he said that the energy use of a fridge should be plateauing and that fridges need not be replaced as often anymore. Replace it now if it is more than 5 years old, and the 250kWh/year one will probably last a good while.

#### Nice knick-knacks for nieces

The final problem of the episode was posed by Matt to Bec regarding buying some Christmas presents for his nieces. He mentioned struggling to find a cool gift for them as he can only think of educational ones. He said they're 7 and 9.

Bec started to list out some gifts she found while researching. First was a Harry Potter-style invisibility cloak with a green cloth inside, which would turn into a green screen using an app, at £60. Second was a Scruff-a-Luv Real Rescue electronic pet, which mimics a rescued animal that you could groom. Thirdly, a smART Pixelator, a pixel art bead toy with an app that helps you pixelise any image. Lastly, she also mentioned the LEGO City Mars Research Shuttle set.

#### TL;DR

Q: "Whats the deal with shoe sizes?"

* UK: Length (in feet) = 12 + (size-12)\*(1/36),
* US (men): Length (in feet) = 13 + (size-12)\*(1/36), US (women): Length (in feet) = 14 + (size-12)\*(1/36),
* EU: Length (cm) = size\*2/3 - 1.5

Q: "What is the most number of (someone's) organs they could sell at the highest price to make the most profit without dying?"

* £361,424.30 without needing medical assistance to live.
* £900,000 with medical assistance to stay alive.

Q: "Given that the general cost of a fridge is electricity, and that fridges become more energy efficient while electricity gets more expensive, how often should one replace their fridge?"

* Replace if it is 5 years older or more.

### Corrections

01:04 - Matt says "early adapter" when he means "early adopter". But it could be both. It’s a podcast that changes you.

18:08 - Bec says "4" instead of "6". Don't worry: the maths was all ok. Phew.

26:22 - Bec says "implicit permission" when she means "explicit permission". She will definitely double check before she repurposes any one else's teeth.