Challenge 1

Problem

A friend of yours is the director of a zoo. She has described you the latest acquisition she was considering for her zoo: a rare colony of chameleons. This colony of chameleons includes 34 red, 35 blue, and 30 green individuals. Whenever two chameleons of different colors meet, each changes to the third color. The color mutation is a unique feature an your friend expects to attract many visitors with this colony. Still, the director considers: if, by any chance, all 99 chameleons are in the same color, the colony will stop being an attraction.

Question: Could this ever happen? Justify your answer

Note: It is not enough to say ‘yes’ or ‘no’. You must provide an explanation.

Prize

Each member of the winning team will receive a one-year membership to the Mathematical Association of America.

Deadline

September 16, 2016, 11.59pm

Rules

Read carefully the rules before creating a team to solve the problem.

Submission

Submit your answers using the following format.