Combinatorics & the Pigeonhole Principle

The Pigeonhole Principle Explained | Built In

What is the pigeonhole principle? - Definition, examples, and proof explained

Pigeonhole Principle - Discrete Mathematical Structures Video Lecture - Computer Science Engineering (CSE)

The Pigeonhole Principle - SlideServe

SOLVED:An alternative proof of Theorem 3 based on the generalized pigeonhole principle is outlined in this exercise. The notation used is the same as that used in the proof in the text. a) Assume that ik ≤n for k=1,2, …, n^2 1 . Use the generalized pigeonhole principle to show that there are n 1 terms ak1, ak2, …, akn 1 with ik1=ik2=⋯= ikn 1, where 1 ≤k1akj 1 for j=1,2, …, n .[Hint: Assume that akj ikj 1, which is a contradiction. ] c) Use parts (a) and (b) to show that if there is no increasi