olymmath

BALTIC-WAY 2015 Problem 8

  • Answer

With inspiration drawn from the rectilinear network of streets in New York, the Manhattan distance between two points (a,b)(a, b) and (c,d)(c, d) in the plane is defined to be

∣a−c∣+∣b−d∣. |a-c|+|b-d| \text {. }

Suppose only two distinct Manhattan distances occur between all pairs of distinct points of some point set. What is the maximal number of points in such a set?

Dataset text NuminaMath olympiads. Quoted with source.

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