MathDB

(065) A3

Part of 1984 Tournament Of Towns

Problems(1)

TOT 065 1984 Spring S-A3 infinite rooms in hallway, finite pianists

Source:

8/19/2019
An infinite (in both directions) sequence of rooms is situated on one side of an infinite hallway. The rooms are numbered by consecutive integers and each contains a grand piano. A finite number of pianists live in these rooms. (There may be more than one of them in some of the rooms.) Every day some two pianists living in adjacent rooms (the Arth and (k+1k +1)st) decide that they interfere with each other’s practice, and they move to the (k−1k - 1)st and (k+2k + 2)nd rooms, respectively. Prove that these moves will cease after a finite number of days.
(VG Ilichev)
combinatorics