# Clue to Puzzle #52: Different Coloured Socks in a Draw.

52. 100 black and white socks are in a drawer. How many socks must you pull out before you are guaranteed to have a pair? Generalize to socks of N different colors.

## Assumptions

To be clear we are assuming socks are either black or white, and a pair constitutes either two black or two white socks.

## The Puzzle

So we need to think about the worst case scenarios after drawing a certain number of socks. If we have taken two socks we could have a pair, or we could have one of each. What about if we pull another sock, and another one.

Extend this to N different colours.

Where next?

© Nigel Coldwell 2004 -  – The questions on this site may be reproduced without further permission, I do not claim copyright over them. The answers are mine and may not be reproduced without my expressed prior consent. Please inquire using the link at the top of the page. Secure version of this page.

PayPal
I always think it's arrogant to add a donate button, but it has been requested. If I help you get a job though, you could buy me a pint! - nigel