IOQM · Mathematics · Combinatorics
Pigeonhole Principle
Simple and generalized pigeonhole and classical olympiad applications.
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- Previous papers: 10 official question papers from HBCSE-TIFR (Mathematical Olympiad Cell) — 2025, 2024, 2022-23, 2021-22 and 1 earlier year.
- Practice: 2 answer-checked practice questions on Pigeonhole Principle for IOQM — practise them.
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Take a full mock →Q1 · Pigeonhole Principle · MEDIUM
Among any n integers chosen from the set {1, 2, 3, ..., 20}, at least two must have a difference that is a multiple of 6. Find the smallest such n.
Q2 · Pigeonhole Principle · HARD
From the set {1, 2, 3, ..., 20}, what is the minimum number of integers that must be chosen to guarantee that at least two chosen integers differ by exactly 5?