word problem

Question

Megan has many gray socks, white socks, and black socks in a drawer. In the dark she pulled out two socks that did not match. How many more socks does Megan need to pull from the drawer to be certain to have a matching pair?

Answer 1

If Megan pulls out two more socks (total four), she will be sure of having a matching pair.

 

This is because there are a total of three categories of socks -- gray, white, and black.  There might possibly be one of each color if show pulls out only three socks.  But, when she pulls out the fourth sock, she can be sure that it matches one of the socks that she already has.

Answer 2

There three colors of socks. Call them A, B, and C.

First pick she gets an A.

Second pick she gets a B.

Third pick she gets a C.

Now the fourth pick must make a pair to one of the first three.

 

She must make four picks to be certain.