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Given a set of n men and n women, marry them off in pairs after each man has ranked the women in order of preference from 1 to n, {w_1,...,w_n} and each women has done ...

Stadium billiards refers to the investigation of the path of a billiard ball on a stadium-shaped billiard table, as first investigated by Bunimovich (1974).

A figurate number of the form StOct_n = O_n+8Te_(n-1) (1) = n(2n^2-1), (2) where O_n is an octahedral number and Te_n is a tetrahedral number. The first few are 1, 14, 51, ...

A string of length n on an alphabet l of m characters is an arrangement of n not necessarily distinct symbols from l. There are m^n such distinct strings. For example, the ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

The tetrahemihexahedron is the uniform polyhedron with Maeder index 4 (Maeder 1997), Wenninger index 67 (Wenninger 1989), Coxeter index 36 (Coxeter et al. 1954), and Har'El ...

Color each segment of a knot diagram using one of three colors. If 1. At any crossing, either the colors are all different or all the same, and 2. At least two colors are ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

The truncated dodecadodecahedron, also called the quasitruncated dodecahedron, is the uniform polyhedron with Maeder index 59 (Maeder 1997), Wenninger index 98 (Wenninger ...

An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...