Question 111
ignoramus arranged 11 positive integers in a circle. for each two adjacent numbers, he calculated 11 results, there are 4 two, 4 two, and 3 three. Prove that ignoramus made a mistake in his calculations. Dunno wrote out 11 natural numbers in a circle. For every two neighboring numbers, he calculated their difference. As a result, among the differences found, four units, four deuces and three triples were found. Prove that Dunno somewhere made a mistake. (R. Zhenodarov)