MathDiscrete mathCombinatorics

The pigeonhole principle

Formulation

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Which of the following statements formulates the pigeonhole principle?

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You can place

n

objects into

m

groups, if there are more groups than objects.

If we distribute

n

objects into

m

groups (

n>m

), there will be at least one group in which there is more than one object.

You can always place pigeons in pigeonholes.

If two pigeons are in the same pigeonhole, then there are fewer pigeonholes than there are pigeons.

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