Prove guaranteed collisions when distributing more items than containers.
npx skills add https://github.com/bneb/perqed --skill pigeonhole-principle
Please help me install this Agent Skill. Skill: pigeonhole_principle Source: https://github.com/bneb/perqed/tree/main/.agents/skills/pigeonhole_principle Command: npx skills add https://github.com/bneb/perqed --skill pigeonhole-principle
The pigeonhole principle asserts that if more objects are placed into fewer containers, at least one container must contain multiple objects, enabling guarantees of collisions or repeated values.
Apply the pigeonhole principle to show that in any distribution of more items than boxes, two items share a box.
High-intent search queries and answers about installing and using this skill.
The pigeonhole principle guarantees a collision by asserting that if more objects are placed into fewer containers, at least one container must hold multiple objects, proving a forced repetition.
You use the pigeonhole principle for a counting proof when you need to demonstrate that a mapping from a larger domain to a smaller codomain forces repetition and guarantees non-injectivity.
Yes, the pigeonhole principle serves as proof scaffolding for Ramsey-type arguments and lower or upper bounds, providing existence guarantees for collisions where domain size exceeds codomain size.
To prove existence, apply the pigeonhole principle to show that in any distribution of more items than boxes, such as 11 items into 10 boxes, at least two items must share a container.
The pigeonhole principle only guarantees non-injectivity when a strict counting constraint is met, meaning it is limited to scenarios where the domain size strictly exceeds the codomain size.
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