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XXIX Rioplatense Mathematical Olympiad

Argentina counting and probability

Problem

Consider the following arrangement of 25 points. • • • • • Gastón must choose 4 of these points. • • • • • The chosen points must be the vertices of a square. • • • • • In how many ways can this be done? • • • • •

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Solution
The following figures show how many squares of each type Gastón can choose. (a) 1 square (b) 16 squares (c) 9 squares (d) 4 squares (e) 9 squares (f) 4 squares (g) 4 squares (h) 2 squares (i) 1 square The total number of squares is 50.
Final answer
50

Techniques

Enumeration with symmetry