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1

Part of 2022 South Africa National Olympiad

Problems(1)

SAMO 2022 Problem 1 - Pairs of points more than 2 units apart

Source: South African Mathematics Olympiad 2022, Problem 1

8/11/2022
Consider 1616 points arranged as shown, with horizontal and vertical distances of 11 between consecutive rows and columns. In how many ways can one choose four of these points such that the distance between every two of those four points is strictly greater than 22?
[asy] for (int x = 0; x < 4; ++x) { for (int y = 0; y < 4; ++y) { dot((x, y)); } } [/asy]
combinatorics