# Sunday Times Teaser 2768 – In the Bag

### by Richard England

#### Published: 11 October 2015 (link)

A set of snooker balls consists of fifteen reds and seven others. From my set I put some into a bag. I calculated that if I picked three balls out of the bag simultaneously at random, then there was a one in a whole-number chance that they would all be red. It was more likely that none of the three would be red — in fact there was also a one in a whole-number chance of this happening.

How many balls did I put in the bag, and how many of those were red?

2. At first I read the puzzle as placing 7 of the non-red balls in the bag, but that doesn’t give any solutions (and makes the question at the end a bit odd).

But if we place only some of the non-red balls in the bag then there is a single solution.

Hi Jim,

I have changed the wording to (hopefully) remove the ambiguity you found.