Black and Blue socks You're late for an evening dinner, and need pair of socks. Your sock drawer contains many black and blue socks, but there's been an electricity blackout and the socks are indistinguishable in the dark. However, by grabbing the right number of socks, you can guarantee to have a matching pair.

The Puzzle: What is the smallest number of socks you need to remove to guarantee that you'll have a pair of black socks or a pair of blue socks?


StumbleUpon Toolbar Stumble It!
Hints and solutions below:

Hints will appear here!

The number of socks required doesn't depend on the number of socks in the drawer (assuming there are a pair of black and blue socks in there!)

Turn the problem on its head. Think about the worst case scenario where, try as you might, with each additional sock you fail to get a matching pair. For how long can you keep up this unfortunate situation?

The simple answer is that you only need to remove three socks to guarantee that you'll have a pair. By taking three socks, they'll either be all black, all blue, 2 blue and one black, or 2 black and one blue.

A common stumbling block is the thought "if my first sock is black, but all the others are blue, then I'm in trouble". But in this situation, though you won't have a black pair of socks, you will have a blue pair.


Logic Puzzles:

The Twelve days of Christmas (*/**) 1 Dec 07
How many gifts did my true love send me?
The squashed bee (**) 15 Oct 07
How far does the bee travel before it's squashed?
12 coins (****) 14 Oct 07
Find the counterfeit coin in 3 moves
Black and blue socks (*) 28th Aug 07
Choose a matching pair of socks in the dark
100 monks (**) 18th Aug 07
How do you communicate simply by not dying?
Coins on a table (***) 15 Aug 07
The last person to place a coin wins
10 Barons (***) 15 Aug 07
Help me catch a cheating Baron by weighing gold bars
Fox, chicken, grain (*) 14 Aug 07
Cross a river taking only one at a time
5 pirates (****) 14 Aug 07
A tricky problem in booty allocation
Try our other Puzzles:

50 states
Our popular 50 states name game.
England counties
Name the 48 ceremonial counties of England.
Asia
53 countries and territories of Asia.