FILE No.91Unsolved
During a blackout, a detective wants a pair of socks. His drawer holds red, blue and black socks, many of each, all mixed up (no left or right).
He cannot see colours. A matching pair is two socks of the same colour.
How many socks must he pull out to be sure of having a matching pair, whatever he draws?
If you get stuck, open the hints one at a time, in order.
With 3 socks, could all be different colours?
What happens with the 4th sock?
Think of the worst case.
How many socks must he pull out to be sure of having a matching pair, whatever he draws?
Choose the answer closest to the truth.
4
The answer is: 4.
With 3 socks they might be red, blue and black, with no pair. The fourth sock must match one of the three colours. Think of the worst case: number of colours + 1.
People imagine lucky draws, so they think 2 socks will do.
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