Problem #PRU-102969

Problems Discrete Mathematics Set theory and logic Mathematical logic Mathematical logic (other)

Problem

The evil stepmother, leaving for the ball, gave Cinderella a bag in which rice and cous-cous were mixed, and ordered for them to be sorted. When Cinderella was leaving for the ball, she left three bags: one was rice, the other – cous-cous, and in the third – an unsorted mixture. In order not to confuse the bags, Cinderella attached to each of them a sign saying: “Rice”, “Cous-cous” and “Mixture”.

The stepmother returned from the ball first and deliberately swapped all the signs in such a way that on every sack there was an incorrect sign. The Fairy Godmother managed to warn Cinderella that now none of the signs on the bags are true. Then Cinderella took out only one single grain from one sack and, looking at it, immediately worked out what was in each bag. How did she do it?