Sunday Times Teaser 2805 – Greek Urns

by Michael Fletcher

Published: 26 June 2016 (link)

I have three Greek urns. I took some balls (consisting of an odd number of red balls and some black balls) and I placed one or more ball in the first urn, one or more in the second, and the rest in the third. If you chose an urn at random and then a ball at random from that urn, then overall there would be a 50 per cent chance of getting a red ball.

Then I moved some black balls from one of the urns to another. In this new situation, if you chose an urn and then a ball there was a 75 per cent chance of getting a red. In fact, with this set of balls and urns it would be impossible to get a higher percentage than that.

How many red balls and how many black balls were there?