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number of ways to cut a 8x8 board

Source: Switzerland - 2015 Swiss MO Final Round p6

January 14, 2023
combinatoricscombinatorial geometry

Problem Statement

We have an 8×88\times 8 board. An interior edge is an edge between two 1×11 \times 1 cells. we cut the board into 1×21 \times 2 dominoes. For an inner edge kk, N(k)N(k) denotes the number of ways to cut the board so that it cuts along edge kk. Calculate the last digit of the sum we get if we add all N(k)N(k), where kk is an inner edge.
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