Pigeonhole principle exercises

Question

I have an exam in combinatorics on Friday and the pigeonhole principle is a part of the material. Can someone give me a reference to a book with the hardest(!) questions on this material? Thank you very much, it can help me a lot!

Here are a few problems. – David Mitra Jun 26 '13 at 16:06 — David Mitra, Jun 26 '13 at 16:06
You probably don't want the hardest such questions. – Thomas Andrews Jun 26 '13 at 16:14 — Thomas Andrews, Jun 26 '13 at 16:14
Duplicate of http://math.stackexchange.com/q/194312/18398 – JRN Jan 16 '14 at 05:15 — JRN, Jan 16 '14 at 05:15

score 1 · Answer 1 · answered May 19 '14 at 18:40

The book "Problem Solving Through Problems" by Loren C. Larson has a section on the pigeonhole principle that I like very much. A favourite application of mine is showing that every 2-colouring of the complete graph on 6 vertices contains a triangle whose edges are all the same colour.

score 0 · Answer 2 · edited May 19 '14 at 17:25

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In the book 'Proofs From THE BOOK' by Aigner & Ziegler there is a chapter on combinatorics which contains some nice problems. Here's a neat problem from 'Combinatorics and Graph Theory' by Harris et al: Let $a_1, a_2, a_3 \dots a_n$ be a sequence of integers. Prove the existence of integers $1\le j\le k\le n$ such that $\sum_{i=j}^k a_i $ is a multiple of $n$.

edited May 19 '14 at 17:25

Community

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answered Jul 03 '13 at 19:24

Sai

417

score 0 · Answer 3 · answered May 19 '14 at 18:32

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One of Paul Erdos's favorites:

We choose $n+1$ numbers from the set $\{1, 2, \cdots, 2n\}$. Prove that there are some two of our $n+1$ numbers such that one divides the other.

answered May 19 '14 at 18:32

Sameer Kailasa

9,171

Pigeonhole principle exercises

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