query: Numbers theory, combinatorics
positive_passages.docid: 19446
positive_passages.text: Number theory question from today's Pre - RMO
negative_passages.docid: 72052
negative_passages.text: Combinatorics the number of options for $k$ different balls in n different cells, with at least $1$ ball in each cell
negative_passages.docid: 139842
negative_passages.text: Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^2\binom{n}{k}=n\times 2^n$
negative_passages.docid: 68882
negative_passages.text: Path to Combinatorics Problem [$1.11$]
negative_passages.docid: 67927
negative_passages.text: Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
negative_passages.docid: 54794
negative_passages.text: British Olympiad; Combinatorics Recursion
negative_passages.docid: 104397
negative_passages.text: Books on Number Theory for Layman
negative_passages.docid: 41726
negative_passages.text: Musical and combinatorial proof
negative_passages.docid: 50550
negative_passages.text: Combinatorics Distribution - Number of integer solutions Concept Explanation
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 6366
negative_passages.text: Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
negative_passages.docid: 134938
negative_passages.text: Committee combinatorics
negative_passages.docid: 13860
negative_passages.text: IMO/1981 - Combinatorics
negative_passages.docid: 10917
negative_passages.text: Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
negative_passages.docid: 33104
negative_passages.text: Combinatorial Proof with Summation Identity
negative_passages.docid: 43076
negative_passages.text: Chess tournament combinatorics
negative_passages.docid: 23523
negative_passages.text: Two problems on number theory