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Discrete Mathematics

Pigeonhole Principle

The pigeonhole principle says that placing more objects than containers forces at least one container to hold multiple objects.

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Meaning

What Is Pigeonhole Principle?

The pigeonhole principle says that placing more objects than containers forces at least one container to hold multiple objects.

The pigeonhole principle says that placing more objects than containers forces at least one container to hold multiple objects.

Examples

Examples of Pigeonhole Principle

113 people guarantee at least two share a birth month.
Understand

Formula and Key Points

Formula / rule
If n+1 objects enter n boxes, one box has at least 2.
  • Know the definition and standard notation for Pigeonhole Principle.
  • Be able to recognise or compute pigeonhole principle in a small example.
  • Connect the concept to nearby topics in the same subject before using it in larger CSE problems.
CSE Connection

Why This Matters in Computer Science

Used in algorithm proofs, counting, recurrence analysis, data structures and theoretical computer science.

FAQ

Pigeonhole Principle: Frequently Asked Questions

What is Pigeonhole Principle?

The pigeonhole principle says that placing more objects than containers forces at least one container to hold multiple objects.

Why is Pigeonhole Principle useful in computer science?

Used in algorithm proofs, counting, recurrence analysis, data structures and theoretical computer science.