Puzzle page

Issue 55
in


socks

Unfortunately I am lazy and disorganised. One symptom of this is that I can never be bothered to fold up my socks in pairs when they come out of the wash. I just chuck them in the drawer. Another symptom is that I always wake up late for work and end up having to rush. Given that I only have white and black socks, how many socks do I have to grab out of my drawer at random to make sure the collection I've grabbed contains a matching pair?

This puzzle is part of the Hands-on risk and probability show, an interactive event culminating in Who Wants to be a Mathionaire? workshop sessions, which you can book to perform at your school. The puzzle appeared in the book How any socks make a pair? by Rob Eastaway.


For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

Comments

3

3
if sock a is white,
and sock b is black,
then sock c can be either black or white and would make a pair

3 2 and a spare in cause you

3
2 and a spare in cause you get a black and a white so you then will either have a pair of white or a pair of black socks

Silly me.

Haha. Even after reading the question several times, I spent ages trying to figure out how to guarantee the guy gets one of each colour, instead of just an individual pair. Anyway my answer for that (wrong) question was 1/2 all socks + 1. ^0^

Ho ho.

3

3
first lets say white
second black
third black or white either one it makes a pair

More colors

Likewise, an extension of the problem is 'how many socks do I have to pull out' if I have three colors? Four? n colors? When you see the solution for all of these, the answer, elegant (to me), is always 'colors + 1'. --That last one will always duplicate one of the previous colors for what is in this case defined as "pair". (Not that I would like to pull out six socks [for five colors] each morning, leaving the remains all over the sink, simply because I was too lazy to pair them in the first place.)

A then more challenging question is 'how many pulls' for two colors, to make THREE identical socks? Or three colors, three socks, etc.

My sOlution

4

2

2

ans

2+2

2+2??

3
first one is lets say black
second is (worst case scenario) white
third one will make a pair with either the first or second sock

third one will make a pair with either the first or second sock

yep

3 is definitely right.

This is a simple application of the pigeonhole principle. If you have k pigeonholes and k+1 pigeons, then one pigeonhole will contain more than one pigeon.