Problem #PRU-64931

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

Problem

Author: E.V. Bakaev

After a hockey match Anthony said that he scored 3 goals, and Ilya only one. Ilya said that he scored 4 goals, and Serge scored 5 goals. Serge said that he scored 6 goals, and Anthony only two. Could it be that the three of them scored 10 goals, if it is known that each of them once told the truth, and once lied?