A draw contains an unsorted collection of black, navy, white, and brown coloured socks. If socks are taken at random, one at a time, what is the minimum number which must be taken to be certain of finding five matching pairs?

Can you obtain a formula to find the minimum number of socks which must be taken to be certain of finding p matching pairs when the draw contains an unsorted collection of c different coloured socks?

This is just a small challenge problem if you wish to think about it.

17

No

sure?

Yes :-)

how?

You can think about it as an induction so step by step. If you take 5 socks out than surely there must be 1 matching. If we take 2 more than again there will be 1 matching for sure. So to get 5 matching we need 3+2*5

This helps making a formula as well

oh, I read the question wrong. I thought you meant five gloves of the same color. fail.

I see, but you can see now that it is not gloves but socks :DD

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