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One of the seven 4-polyhexes. S. Kim has observed that four worms solve the puzzle of finding a non-three-colorable map with only four congruent countries (as long as no ...

1 1 2 2 3 5 5 7 10 15 15 20 27 37 52 The Bell triangle, also called Aitken's array or the Peirce triangle (Knuth 2005, p. 28), is the number triangle obtained by beginning ...

A series which is not convergent. Series may diverge by marching off to infinity or by oscillating. Divergent series have some curious properties. For example, rearranging ...

A dissection of a rectangle into smaller rectangles such that the original rectangle is not divided into two subrectangles. Rectangle dissections into 3, 4, or 6 pieces ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

A plane path on a set of equally spaced lattice points, starting at the origin, where the first step is one unit to the north or south, the second step is two units to the ...

The impossible fork (Seckel 2002, p. 151), also known as the devil's pitchfork (Singmaster), blivet, or poiuyt, is a classic impossible figure originally due to Schuster ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

The paradox of a man who states "I am lying." If he is lying, then he is telling the truth, and vice versa. Another version of this paradox is the Epimenides paradox. Such ...

A game which is played by the following rules. Given one or more piles (nim-heaps), players alternate by taking all or some of the counters in a single heap. The player ...