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Arrange copies of the n digits 1, ..., n such that there is one digit between the 1s, two digits between the 2s, etc. For example, the unique (modulo reversal) n=3 solution ...

A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

Take any triangle with polygon vertices A, B, and C. Pick a point A_1 on the side opposite A, and draw a line parallel to BC. Upon reaching the side AC at B_1, draw the line ...

The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a ...

A game played with two dice. If the total is 7 or 11 (a "natural"), the thrower wins and retains the dice for another throw. If the total is 2, 3, or 12 ("craps"), the ...

Gödel's first incompleteness theorem states that all consistent axiomatic formulations of number theory which include Peano arithmetic include undecidable propositions ...

The recursive sequence defined by the recurrence relation a(n)=a(a(n-1))+a(n-a(n-1)) (1) with a(1)=a(2)=1. The first few values are 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, ... (OEIS ...