Y by Adventure10, Mango247
The Judgment of the Council of Sages proceeds as follows: the king arranges the sages in a line and places either a white hat or a black hat on each sage's head. Each sage can see the color of the hats of the sages in front of him, but not of his own hat or of the hats of the sages behind him. Then one by one (in an order of their choosing), each sage guesses a color. Afterward, the king executes those sages who did not correctly guess the color of their own hat. The day before, the Council meets and decides to minimize the number of executions. What is the smallest number of sages guaranteed to survive in this case?
See also http://www.artofproblemsolving.com/Forum/viewtopic.php?f=42&t=530553
See also http://www.artofproblemsolving.com/Forum/viewtopic.php?f=42&t=530553