query: Given a $3 \times n$ board, find the number of ways to fill it with $2\times1$ rectangular boxes.
positive_passages.docid: 24370
positive_passages.text: Dominos ($2 \times 1$ on $2 \times n$ and on $3 \times 2n$)
negative_passages.docid: 103190
negative_passages.text: Algorithm to get the maximum size of n squares that fit into a rectangle with a given width and height
negative_passages.docid: 45448
negative_passages.text: Minimum number of $k$-partitions of a set of size $n$ to enumerate all $n \choose k$ combinations
negative_passages.docid: 57822
negative_passages.text: Number of ways to choose two disjoint subsets of a set
negative_passages.docid: 66842
negative_passages.text: Number of $n^2\times n^2$ permutation matrices with a 1 in each $n\times n$ subgrid
negative_passages.docid: 58975
negative_passages.text: How many rectangles can be obtained by joining four of the $12$ vertices of a $12$-sided regular polygon?
negative_passages.docid: 111609
negative_passages.text: Each $2\times 5$ rectangle contains $1\times 3$ rectangle
negative_passages.docid: 18482
negative_passages.text: Can the squares with side $1/n$ be packed into a $1 \times \zeta(2)$ rectangle?
negative_passages.docid: 17097
negative_passages.text: Number of moves necessary to solve Rubik's cube by pure chance
negative_passages.docid: 9411
negative_passages.text: Number of permutations of $n$ elements where no number $i$ is in position $i$
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: 155372
negative_passages.text: Find the number of permutations in $S_n$ containing fixed elements in one cycle
negative_passages.docid: 84865
negative_passages.text: A 5x5 board has 25 cells.The numbers $\{1,2,3,4,5\}$ are written on every row,every column and the two main diagonals.
negative_passages.docid: 60661
negative_passages.text: How to solve this combination problem quickly?
negative_passages.docid: 139913
negative_passages.text: In how many ways can $5$ balls of different colours be placed in $3$ boxes of different sizes if no box remains empty?
negative_passages.docid: 141090
negative_passages.text: Interview question: three arrays and O(N*N)
negative_passages.docid: 71221
negative_passages.text: Find a recurrence relation for the number of ways to arrange $n$ dominoes to fill a $2$ by $n$ checkerboard.