2. (7-8 grades) Each inhabitant of the island is either a knight, who always tells the truth, or a liar, who always lies. One day, 50 islanders sat around a round table, and each one said whether their right-hand neighbor was a knight or a liar. In this case, the residents sitting in the $1-\mathrm{m}, 3-\mathrm{m}, \ldots$ and $49-\mathrm{m}$ places said “Knight,” while those sitting in the 2-nd, 4-th, ... and 48-th places said “Liar.” What could the resident sitting in the 50-th place have said? (The places are numbered in a circle, starting from some point.)
Answer: "Knight".

Solution. It is enough to consider two cases, who the first one was - a knight or a liar.

1) If the first one is a knight, then from the given statements we get a chain of those sitting at the table: RRLLRRLLRR...: pairs of knights and liars alternate. Since the total number of inhabitants is 50 - not a multiple of 4, the last one is a knight and he should honestly say about the first one, that is, call him a knight.
2) If the first one is a liar, then similarly we get a chain of alternating pairs of liars and knights, in which the first and last are liars, so the answer of the last one is again "Knight".