MathDB

There are

N\ge3

letters arranged in a circle, and each letter is one of

L

T

and

F

. For a letter, we can do the following operation: if its neighbors are the same, then change it to the same letter too; otherwise, change it so that it is different from both its neighbors. Show that for any initial state, one can perform finitely many operations to achieve a stable state. Here, a stable state means that any operation does not change any of the

N

letters. (ltf0501)

C2

Problems(1)