Sock Drawer Quiz Puzzle

This week's puzzle concerns the Quiz Master Shop sock drawer.

We only have black or white socks, and we put them, unpaired, in the communal sock drawer. There is something strange about the number of each colour of socks in the drawer - if we take out two socks at random, there is exactly a 50% chance that they are both black. How many socks of each colour do we have?

Once you've worked out a solution (quite quickly we hope) you will realise that we can't have that small a number of socks. There would not be enough to share between us. In fact the number of socks we have is in double figures.So now work out how many socks of each colour we have.

As a further puzzle, work out how many black socks and how many white socks we would need such that there is a 50% chance of three randomly selected socks all being black.

Is there another solution for this with higher numbers, in the same way as for two random socks?

Can you work out a general solution for four, five, six socks etc.?

As usual you can post the answers as a comment on this website, reply to the post on Facebook, or retweet or reply on Twitter @quizmastershop.

Answer at 9.00 on Monday


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