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There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

Go is played on a 19×19 grid, with pieces being placed at the intersections of grid lines, rather than in the middle of them. Go boards have a number of peculiarities, ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

The Jacobsthal numbers are the numbers obtained by the U_ns in the Lucas sequence with P=1 and Q=-2, corresponding to a=2 and b=-1. They and the Jacobsthal-Lucas numbers (the ...

The m×n king graph is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a king. The number ...

The pentaflake is a fractal with 5-fold symmetry. As illustrated above, five pentagons can be arranged around an identical pentagon to form the first iteration of the ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

A totalistic cellular automaton is a cellular automata in which the rules depend only on the total (or equivalently, the average) of the values of the cells in a ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...