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?
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.
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