query: Combinatorics pigeonhole principle with matrix
positive_passages.docid: 154494
positive_passages.text: Prove that there exists a row or a column of the chessboard which contains at least √n distinct numbers.
negative_passages.docid: 39746
negative_passages.text: How to prove that given set is a connected subset of the space of matrices?
negative_passages.docid: 134599
negative_passages.text: How do I do Combinatorics / Counting?
negative_passages.docid: 13860
negative_passages.text: IMO/1981 - Combinatorics
negative_passages.docid: 75852
negative_passages.text: Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other
negative_passages.docid: 22776
negative_passages.text: Squares in Matrix
negative_passages.docid: 91938
negative_passages.text: Countable Matrix Representation
negative_passages.docid: 107110
negative_passages.text: Solving Rubik's cube and other permutation puzzles
negative_passages.docid: 39724
negative_passages.text: Combinatorial Identities
negative_passages.docid: 41205
negative_passages.text: Help me solve a combinatorial problem
negative_passages.docid: 142978
negative_passages.text: combinatorics: sum of product of integer compositions
negative_passages.docid: 51638
negative_passages.text: pigeonhole principle divisibility proof
negative_passages.docid: 97254
negative_passages.text: What is the proof of permutations of similar objects?
negative_passages.docid: 70282
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
negative_passages.docid: 158860
negative_passages.text: Subsetting matrices
negative_passages.docid: 113953
negative_passages.text: Circular permutations with indistinguishable objects
negative_passages.docid: 15452
negative_passages.text: Proving determinant product rule combinatorially