## Counting Puzzles

1. X is a set with n elements. Find the number of triples (A, B, C), where A, B, C are subsets of X, such that A is a subset of B and B is a subset of C.

2. Let m and n be integers greater than 1. Consider an m*n rectangular

grid of points in the plane. Some k of these points are colored red in such a

way that no three red points are the vertices of a right-angled triangle, two of

whose sides are parallel to the sides of the grid. Determine the greatest

possible value of k for any given values of m,n > 1.

Source: unknown

View the solution

Reconstruct the Numbers

A Set of Rational Numbers

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