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MathNet 2020 — Math Olympiad Vault — Part 06 Question 100

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 06

Question 100

The chessboard was split into domino tiles, meaning it was split into $1 \times 2$ and $2 \times 1$ rectangles. Each tile has a number written on it equal to the number of tiles that it has a common line segment with, without taking into account the tile itself. What is a least possible sum of all numbers that are written on the chessboard?
(Arsenii Nikolaiev)