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2 in 8 points whose distnce <5 inside a 7x12 rectangle

Source: New Zealand NZMOC Camp Selection Problems 2018 p3

September 19, 2021
combinatorial geometrygeometryrectanglecombinatorics

Problem Statement

Show that amongst any 8 8 points in the interior of a 7×127 \times 12 rectangle, there exists a pair whose distance is less than 55.
Note: The interior of a rectangle excludes points lying on the sides of the rectangle.
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