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In identical experiments, an Allais paradox occurs when the addition of an independent event influences choice behavior. Consider the choices in the following table (Kahneman ...

The cuban primes, named after differences between successive cubic numbers, have the form n^3-(n-1)^3. The first few are 7, 19, 37, 61, 127, 271, ... (OEIS A002407), which ...

If S_1, S_2, and S_3 are three conics having the property that there is a point X, not on any of the conics, lying on a common chord of each pair of the three conics (with ...

Guy's conjecture, which has not yet been proven or disproven, states that the graph crossing number for a complete graph K_n is ...

A positive integer which is divisible by the sum of its digits, also called a Niven number (Kennedy et al. 1980) or a multidigital number (Kaprekar 1955). The first few are ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

The problem of determining how many nonattacking knights K(n) can be placed on an n×n chessboard. For n=8, the solution is 32 (illustrated above). In general, the solutions ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

A pseudoperfect number, sometimes also called a semiperfect number (Benkoski 1972, Butske et al. 1999), is a positive integer such as 20=1+4+5+10 which is the sum of some (or ...