Problem #PRU-88030

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

Problem

The stepmother, leaving for the ball, gave Cinderella a sack which contained a mixture of poppy and millet, and ordered them to be sorted. When Cinderella was leaving for the ball, she left three sacks: one contained millet, the other contained poppy, and in the third – a mixture that had not yet been sorted. In order not to confuse the sacks, Cinderella attached a label to each of them that said: “Poppy seed”, “Millet” and “Mixture”. The stepmother returned from the ball first and deliberately swapped all of the labels in such a way that on each sack there was an incorrect inscription. The fairy godmother managed to warn Cinderella that now none of the labels on the sacks were correct. Then Cinderella took out only one single grain from one sack and, looking at it, immediately guessed what was in each sack. How did she do this?