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A connected labeled graph with n graph edges in which all graph vertices can be labeled with distinct integers (mod n) so that the sums of the pairs of numbers at the ends of ...

A purple cow is a confirming instance of the hypothesis that all crows are black.

A polyiamond composed of six equilateral triangles. The 12 hexiamonds are illustrated above. They are given the names bar, crook, crown, sphinx, snake, yacht, chevron, ...

An algorithm for finding a graph's spanning tree of minimum length. It sorts the edges of a graph in order of increasing cost and then repeatedly adds edges that bridge ...

The unique magic square of order three. The Lo Shu is an associative magic square, but not a panmagic square.

A general formula giving the number of distinct ways of folding an m×n rectangular map is not known. A distinct folding is defined as a permutation of N=m×n numbered cells ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

A pandiagonal semiperfect magic cube is a semiperfect magic cube that remains semiperfect when any single orthogonal section is "restacked" cyclically so that the ordering of ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...