Copyright © University of Cambridge. All rights reserved.

'Chameleons' printed from http://nrich.maths.org/

Show menu

On a certain island there are 12 green, 15 brown and 18 yellow chameleons. Whenever two chameleons of different colours meet they always change colour to the third colour (e.g. a brown and a yellow would both change to green when they met). This is the only time they change colour. Describe the shortest sequence of meetings in which all the chameleons change to green.

Now suppose there are 13 green, 15 brown and 17 yellow chameleons and they change colour in exactly the same circumstances. Is it possible now for all the chameleons eventually to be the same colour?