Problem #PRU-64370

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

Problem

Authors: Folklore

There are 13 pupils in the school of witchcraft and wizardry. Before the Clairvoyance exam, the teacher put them at a round table and asked to guess who would receive the clairvoyant’s diploma. The students said nothing about themselves and two of their neighbours, but they wrote the following about all of the others: “None of these ten will get the diploma!" Of course, all of those who passed the exam guessed correctly, and all of the other students were mistaken. How many wizards received a diploma?