## Question

"My socks never stay together in the wash. One always disappears. Is there a scientific explanation for where those socks go? Why are they so unhappy in monogamous relationships?"

## Answer

**It's time for Question of the Week and we received this question from Chani. Izzie Clarke asked Rob Eastaway, mathematician and author of "How Many Socks Make A Pair", to sort out the odds...**

Izzie - I can completely relate to Chani’s question. I’m particularly bad at losing socks. And even if a matching pair make it to the washing machine, I’m often only left with one after a spin. But WHY?

On the Naked Scientists forum ChiralSPO says “personally, I blame entropy…” that’s when - over time - a system becomes more disordered

Whilst Colin2B says “It is well known that in the presence of washing powder in a controlled environment a pair of socks will decay into a single sock and a lump of fluff”

It’s over to Rob Eastaway, mathematician and author of “How Many Socks Make a Pair?”

Rob - The reason why socks disappear is down to the scientific principle known as Murphy's Law - essentially "Anything that can go wrong will go wrong". It turns out that it is statistically likely that even if you start with socks in pairs, you will lose some and are then left with numerous odd socks. Let's suppose you have four pairs of socks: red, blue, green and white. And let's also assume that every time you wash your socks, the machine randomly loses one of them (which is a phenomenon everyone is familiar with)...

Izzie - This actually happens!! Our washing machines are also sock munching monsters. Small items can slip through that hick, rubber ring on front-loading washers that creates a tight seal when the door closes. Back to Rob to crunch the numbers…

Rob - Given that you start with four pairs, the first sock that the machine loses - let's say it's a red sock - is 100% certain to leave you with an odd sock. Now you have seven socks left, three pairs plus an odd red sock. The chance that the next sock you lose belongs to one of the remaining pairs is 6/7… Six socks out of seven are in a pair, which is about 85%.

Izzie - So already, after two washes, there is an 85% chance that you have created two odd socks. And it goes on.

Rob - After the third wash, with four of the six remaining socks still in a pair, there is a 4/6, or two thirds, chance that the third lost sock will also create an odd sock. In other words, after three washes, there's a higher than 50% chance that you'll now have three odd socks.

And the more different pairs of socks you start with, the higher the odds of producing odd socks becomes.

Izzie - Luckily Rob has a tip for solving this problem and fighting the odds…

Rob - Always buy socks that are one colour. You'll still lose socks at the same rate, but this time you won't notice it's happening!

Izzie - Thanks Rob, next time we’re digging for an answer to Aidan’s glowing question.

Aidan - *Consuming orange carrots in high excess can turn your skin orange, because of the beta-carotene. What about purple carrots?*

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