pigeonhole principle

The pigeonhole principle tells us that they cannot all play for different teams.

For instance, the pigeonhole principle is of this form.

It is an advanced generalization of the pigeonhole principle.

This theorem is a consequence of the pigeonhole principle.

The pigeonhole principle arises in computer science.

By the Pigeonhole principle, there must exist an algorithm so that , concluding the proof.

Alice can use the Pigeonhole principle to deduce that her opponent must have at least one S.

The proofs of these lemmas typically require counting arguments such as the pigeonhole principle.

It is a class of search problems that can be shown to be total by an application of the pigeonhole principle.

By operation of the pigeonhole principle, no lossless compression algorithm can efficiently compress all possible data.

Note that it is the pigeonhole principle that guarantees that a solution must exist.

These resemble certain forms of counting found in discrete mathematics and, appropriately, make use of the pigeonhole principle.

Given that this sequence is infinite and the length is bounded, it must eventually repeat due to the pigeonhole principle.

By the pigeonhole principle, there are two blocks among the first 33 blocks that are colored identically.

Because of the pigeonhole principle, every lossless data compression algorithm will end up increasing the size of some inputs.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are 366 possible birthdays, including February 29).

There are polynomial-size Frege proofs of the pigeonhole principle (Buss 1987).

This is a straightforward application of the pigeonhole principle: if a function is r-to-1, then after queries we are guaranteed to have found a collision.

Examples include Harnack's principle, the least upper bound principle, and the pigeonhole principle.

PPP is a complexity class, standing for "Polynomial Pigeonhole Principle".

(The pigeonhole principle again.)

A reversible logic gate of n input bits must have n output bits, by the pigeonhole principle.

"Polynomial size proofs of the propositional pigeonhole principle", Journal of Symbolic Logic 52, pp.

The pigeonhole principle often ascertains the existence of something or is used to determine the minimum or maximum number of something in a discrete context.

Pick a vertex v. There are 5 edges incident to v and so (by the pigeonhole principle) at least 3 of them must be the same colour.