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The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions.
For example, when d=4, the hash table for two occurrences of d would contain the key-value pair 8 and 4+4, and the one for three occurrences, the key-value pair 2 and (4+4)/4 (strings shown in bold). The task is then reduced to recursively computing these hash tables for increasing n , starting from n=1 and continuing up to e.g. n=4.
Josephine's Problem is another good example of a general case. If there is only 1 unfaithful husband, then every woman in the Kingdom knows that except for his wife, who believes that everyone is faithful. Thus, as soon as she hears from the Queen that unfaithful men exist, she knows her husband must be unfaithful, and shoots him.
This sum can also be found in the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle [50]), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows ...
Each problem takes a Boolean formula as input and the task is to compute the number of satisfying assignments. This can be further generalized by using larger domain sizes and attaching a weight to each satisfying assignment and computing the sum of these weights. It is known that any complex weighted #CSP problem is either in FP or #P-hard. [32]
The most famous problem of this type is the eight queens puzzle. Problems are further extended by asking how many possible solutions exist. Further generalizations apply the problem to NxN boards. [3] [4] An 8×8 chessboard can have 16 independent kings, 8 independent queens, 8 independent rooks, 14 independent bishops, or 32 independent ...
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A dominating set of the queen's graph corresponds to a placement of queens such that every square on the chessboard is either attacked or occupied by a queen. On an chessboard, five queens can dominate, and this is the minimum number possible [4]: 113–114 (four queens leave at least two squares unattacked). There are 4,860 such placements of ...