Question

A drawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. What is the least number of socks you must choose, without looking, to be certain that you have chosen two brown socks?

Answer 1

The only time you can be so certain that you have picked 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have picked 2 brown socks, you must pick all 12 white socks and all 18 black socks and only then you can pick 2 brown socks without looking. Therefore the total number of socks that should be picked is:

Total number of socks = 12 white socks + 18 black socks + 2 brown socks

Total number of socks = 32 socks

A total picking of 32 socks is required to be certain without looking that 2 brown have already been chosen.