Question 7
Chameleons on an island have five possible colors. When one bites another, only the bitten chameleon changes color, according to a fixed rule depending solely on their two current colors. Suppose2023 initially red chameleons can, by a sequence of bites among themselves, all become blue. Find the smallest$k$ for which one can always guarantee that$k$ initially red chameleons can all become blue under the same rule.
For example, a rule might say that a red chameleon biting a green one turns the victim blue; a green one biting a red one leaves the victim red; a red one biting a red one turns the victim yellow. Other rules are possible.
For example, a rule might say that a red chameleon biting a green one turns the victim blue; a green one biting a red one leaves the victim red; a red one biting a red one turns the victim yellow. Other rules are possible.