# 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?

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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.

Is it possible to solve teasers without a computer? Most weeks, I try and fail. I have a first class degree in economics and am reasonably numerate. Maslanka’s puzzles in saturday’s Guardian are more user friendly.

Hi Ronan,

If your interest is in solutions without programming, you might prefer the other site I run at https://sites.google.com/site/sundaytimesteasers/. Most contributors there are solving manually and you will often find some good discussions of different approaches.