MathDB

The Sultan gathered

300

court sages and offered them a test. There are caps of

25

different colors, known in advance to the sages. The Sultan said that one of these caps will be put on each of the sages, and if for each color write the number of caps worn, then all numbers will be different. Every sage can see the caps of the other sages, but not own cap. Then all the sages will simultaneously announce the supposed color of their cap. Can sages advance agree to act in such a way that at least

150

of them are guaranteed to name a color right?

Problem Statement