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Socks in the dark

BrainteasersEasy

A drawer holds $10$ black, $8$ grey and $6$ white socks, all loose and mixed. In the dark you pull out socks one at a time without looking. What is the fewest number of socks you must pull out to be sure of having at least $3$ socks of the same colour?

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Hint

Imagine the unluckiest possible sequence of draws.

Solution

In the worst case you avoid $3$ of a colour for as long as possible by taking at most $2$ of each colour.
Every colour has at least $2$ socks, so the unlucky run can reach $3 \times 2 = 6$ socks.
The next sock must be the $3$ rd of some colour, so the answer is $6 + 1 = 7$ .

Answer: $7$

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