Quentin L. Meunier

Problem 1020

Around Table 1 sit sixteen inhabitants of the Logic planet, whose population is exclusively composed of Sinceres (the S, who always tell the truth) and Liars (the M, who always lie).

The sixteen guests in Table 1 say the same sentence: "My two immediate neighbours are M".

1A, 1B, 1C. How many liars are there around table 1 ?

The twelve guests in Table 2 also say the same sentence: "My two immediate neighbours are M and S".

2A, 2B, 2C. How many liars are there around table 2?

Around table 3, there are only eight guests. Four of them say "My two immediate neighbours are M" while the other four say, "My two immediate neighbours are M and S".

3A, 3B, 3C. How many liars are there around table 3?

For each question, if there are several possible answers, order them from the smallest to the largest by stopping at the third (box C), even if there are more than 3 answers.

For this problem, an exhaustive enumeration is largely feasible (2¹⁶ cases for question 1, 2¹² for question 2, 2^C₈⁴ at worst for question 3).

The program, available here, displays all the configurations found, but the display could be limited to one confiugration by number of liars.

Remarque : For this problem, I did not have all the points because of a lack of proofreading the code, in which I initially put a 'and' instead of a 'or' in one place, which had the effect of not displaying all the correct configurations.

1A, 1B, 1C. 8, 9, 10.
2A, 2B. 4, 12.
3A, 3B, 3C. 3, 4, 5.