Ares vs the One Hundred Thebans
Prologue
Ares’ curse, the god of war, has befallen Thebes and the descendants of its founder Cadmus. The city drew the wrath of the great god, cursed since its foundation because it was born from an unusual sowing: the hero Cadmus, following Apollo’s advice, had discovered the mythical Boeotian serpent, killed it, and sowed its teeth into the ground. From these teeth soaked in dark blood, the majestic city of Thebes was born, always loyal to Dionysus, the god of wine and ecstasy. However, Ares, to whom the serpent was consecrated, had sworn vengeance. For this reason, he has persecuted the Theban people for centuries, favoring the dark plots of Fate.
Description
The latest trick devised by the god is the enigma of the stairs. One hundred Thebans are lined up on the staircase overlooking the temple of Dionysus, all facing the bottom of the staircase. On each citizen, a white or black stone is placed. Each citizen can see all the colors of the stones placed on the people in front of him on the stairs, but cannot see his own or the one behind him. The question posed by Ares to each citizen, starting from the one at the top of the stairs, is: “What color is your stone?” If the citizen guesses correctly, they are spared; if they are wrong, they are swallowed by the stairs and lose their life. When the question is asked, all citizens can hear the answer and know whether the responder guessed correctly or lost their life. Before starting this ritual, Ares gives the citizens the time of an hourglass to discuss among themselves and find a common strategy to survive this test.
The Question
What is the strategy that the 100 citizens of Thebes adopt to ensure that 99 of them survive with mathematical certainty, while the last one has a 50% chance of surviving?
FAQ
- It is not known beforehand how many white and black stones there are. At its extreme, it is also possible that all the stones are of one color.
- Citizens can communicate only during the time allowed before the ritual, but not during the test itself.
- There is no way to send signals or messages between citizens once the ritual has started.
- Citizens can only say “white” or “black”.
- Citizens cannot wait for time or use any other trick to pass information other than mere binary information.
- Each citizen can only see the hats of the people in front of him on the stairs.