Question 6
There are 300 sages and 25 possible hat colours. Each sage wears one hat and sees all the other hats but not their own. They know that the numbers of hats of the 25 colours are pairwise different. They must simultaneously guess their own colours. Can they agree in advance on a strategy guaranteeing at least 150 correct guesses? (8 points)
Neutral editorial illustration.
Neutral editorial illustration.