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Border between horizontal and vertical dominoes

Source: Kvant Magazine No. 9 2019 M2576

March 14, 2023
combinatoricsdominoesKvant

Problem Statement

A 8×88\times 8 board is divided in dominoes (rectangles with dimensions 1×21 \times 2 or 2×12 \times 1).
[*] Prove that the total length of the border between horizontal and vertical dominoes is at most 5252. [*] Determine the maximum possible total length of the border between horizontal and vertical dominoes.
Proposed by B. Frenkin, A. Zaslavsky, E. Arzhantseva
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