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3

Part of 2017 China Second Round Olympiad

Problems(1)

Minimal number of separating edges in a tri-colored grid

Source: China Second Round 2017(A), Test 2, Problem 3

2/22/2018
Each square of a 33×3333\times 33 square grid is colored in one of the three colors: red, yellow or blue, such that the numbers of squares in each color are the same. If two squares sharing a common edge are in different colors, call that common edge a separating edge. Find the minimal number of separating edges in the grid.
combinatorics