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1

Part of 1987 Polish MO Finals

Problems(1)

\sum |P_{i-1} - P_i|^2 \le 4 for n points inside a square

Source: 1987 Polish MO Finals p1

1/20/2020
There are n≥2n \ge 2 points in a square side 11. Show that one can label the points P1,P2,...,PnP_1, P_2, ... , P_n such that ∑i=1n∣Pi−1−Pi∣2≤4\sum_{i=1}^n |P_{i-1} - P_i|^2 \le 4, where we use cyclic subscripts, so that P0P_0 means PnP_n.
combinatorial geometrycombinatoricsgeometrysquarepointsdistance