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Is there a set of points on the plane such that every real number appears as a distance between exactly one pair of them?

Given a single triangle on the plane, you can always find a line that bisects it (i.e. that cuts it into two parts of equal areas):

But given two ...

A graph has countably many vertices. However, any finite subgraph of the graph can be colored with at most 4 colors.

Can the entire graph be colored with 4 colors?

Five monkeys in a circus are sitting in the following order:

The ringmaster wants to reverse their order, but only by swapping the positions of two monkeys at a time ...

In a box, there are three red and two green hats. Four logiciansâ€”Alice, Bob, Carol, Davidâ€”pick one hat each from the box without looking and put them on ...

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