Question 12
Twelve people receive twelve different positive integers. In the first round, person 1 says “My number is bigger than 1”, person 2 says “My number is bigger than 2”, and so on, up to person 12 saying “My number is bigger than 12”.
In the second round their responses, in random order, are “My number is less than 1”, “My number is less than 2”, …, “My number is less than 12”. Each person is either always truthful or always lying. Excluding the host, what is the largest possible number of truth-tellers?
In the second round their responses, in random order, are “My number is less than 1”, “My number is less than 2”, …, “My number is less than 12”. Each person is either always truthful or always lying. Excluding the host, what is the largest possible number of truth-tellers?