Problem

Source: St. Petersburg MO 2000, 9th grade, P1

Tags: combinatorics, algebra



On the two sides of the road two lines of trees are planted. On every tree, the number of oaks among itself and its neighbors is written. (For the first and last trees, this is the number of oaks among itself and its only neighbor). Prove that if the two sequences of numbers on the trees are equal, then sequnces of trees on the two sides of the road are equal Proposed by A. Khrabrov, D. Rostovski