total number of solutions for 8 queens problem
Eight queens puzzle The problem of finding all solutions to the 8-queens problem can be quite computationally expensive, as there are 4,426,165,368 (i.e., 64C8) possible arrangements of eight queens on an 8Ã—8 board, but only 92 solutions. It is possible to use shortcuts that reduce computational requirements or rules of thumb that avoids brute-force computational techniques. For example, by applying a simple rule that constrains each queen to a single column (or row), though still considered brute force, it is possible to reduce the number of possibilities to 16,777,216 (that is, 88) possible combinations. Generating permutations further reduces the possibilities to just 40,320 (that is, 8!), which are then checked for diagonal attacks.
Queen mother A new reigning king would have (at accession or eventually) a wife who would be the new queen consort; and, of course, a queen regnant would also be called 'queen'. More to the point, there may be more than one queen dowager at any given time.