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The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

A polyhex consisting of hexagons arranged along a line.

The 4-polyhex illustrated above.

A canonical brick is a 1×2×4 cuboid.

A solitaire game played with cards. The chance of winning is 1/13, and the arithmetic mean of the number of cards turned up is 42.4.

An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ("heads" H or "tails" T) ...

A fractal curve of infinite length which bounds an area twice that of the original square.

A 6-piece polycube dissection of the 3×3 cube.

The problem of determining (or counting) the set of all solutions to a given problem.

The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...