# Sunday Times Teaser 3114 – Colourful Characters

*by Danny Roth*

#### Published Sunday May 29 2022 (link)

George and Martha have recently taken a great-grandchild to a toddler’s birthday party. The youngsters like to traipse around over a pen with a large number of brightly coloured plastic balls. Actually there were 200 in total, some of red, yellow, blue and green. There were at least 30 but fewer than 70 of each colour, with the following properties:

**Red** – perfect square

**Yellow** – prime number

**Blue** – palindromic number

**Green** – divisible by three single-digit prime numbers

George told Martha the above information and the number of red balls. Martha was then able to work out the numbers of each of the others.

How many of each colour were there?

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