query: Opening and closing $100$ doors in multiples of $1,2,3,\ldots$
positive_passages.docid: 4592
positive_passages.text: Prison problem: locking or unlocking every $n$th door for $ n=1,2,3,...$
negative_passages.docid: 26569
negative_passages.text: Counting binary operations on a set with $n$ elements
negative_passages.docid: 124890
negative_passages.text: Divisibility within a block of natural numbers
negative_passages.docid: 28496
negative_passages.text: Generating the partitions of a number
negative_passages.docid: 88356
negative_passages.text: Number of options to distribute $N$ different balls to $K$ numbered cells
negative_passages.docid: 5448
negative_passages.text: Finding the closure of some subsets of the ordered square
negative_passages.docid: 34334
negative_passages.text: Combinatorics Problem with symbols and spaces
negative_passages.docid: 77200
negative_passages.text: Prove:that in any set of 1009 positive integers exits two numbers $a_i$ and $a_j$ such that $a_i-a_j$ or $a_i+a_j$ is divisible by 2014
negative_passages.docid: 35864
negative_passages.text: Playing with numbers form $1$ to $n^2$ in an $n\times n$ grid
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 104603
negative_passages.text: Integer program in which at least one of three inequalities holds
negative_passages.docid: 37629
negative_passages.text: Combinatorial card game
negative_passages.docid: 108919
negative_passages.text: Numbers till 400 divisible by 2, 3, 5, 7
negative_passages.docid: 82958
negative_passages.text: Maximize the product of the partitions of an integer
negative_passages.docid: 144079
negative_passages.text: Find Total number of ways out of N Number taking K numbers every M interval
negative_passages.docid: 24370
negative_passages.text: Dominos ($2 \times 1$ on $2 \times n$ and on $3 \times 2n$)
negative_passages.docid: 150652
negative_passages.text: Number of 4-digit numerals with at most 2 different digits