Vera has $10$ white socks, $10$ black socks, $10$ brown socks, $10$ blue socks, and $10$ red socks. How many socks (at a minimum

Question

2 years ago

6

) must she pull out of her sock drawer to ensure at least two pairs of matching socks

1 answer:

UNO [17] · Answer 1 · 2023-08-22T12:46:34+03:00

The minimum number of socks that she needs to get such that a pair is always formed is 5.

<h3></h3><h3>How many socks must she get to be ensured of having a pair?</h3>

We know that she has:

First, we need to compute the maximum number of socks she needs to take in such a case that no pair is formed.

That will be 4, and represents the case where:

1 white sock, 1 black sock, 1 brown sock, and 1 blue sock are drawn. At that point, no pairs are formed.

Now, if she draws another sock, a pair will always be formed.

From this, we conclude that if she draws 5 socks, always at least one pair will be formed.

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