How many socks take from the shelf to ensure that at least 2 of them have the same colour?


Solution 1

In the worst case, you may pick 6 socks each of a different color. So in order to get at least two socks on the same color, you need to pick at least 7 socks. It's a simple application of the Pigeon hole principle.

Solution 2

Hint: In the worst case scenario, you select from a different pair each time until you run out of pairs, then select one more sock.   Only if you select this many socks, are you guaranteed to have at least a matching pair.

Solution 3

Seven. Worst case: You get one of each color (six), then the seventh must match one of the others.


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Updated on December 07, 2020


  • helloworld
    helloworld almost 3 years

    I'm a little unsure on how to approach this question:

    A drawer shelf contains 6 pairs of socks, each pair a diff color How many socks should be taken from the shelf to ensure that at least 2 of them are of the same?

    Could I use a combination for this? $C(6, 2) = 15$? Thanks in advance!