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.
Yellowjacket Yellowjackets are social hunters living in colonies containing workers, queens, and males (drones). Colonies are annual with only inseminated queens overwintering. Fertilized queens are found in protected places such as in hollow logs, in stumps, under bark, in leaf litter, in soil cavities, and in man-made structures. Queens emerge during the warm days of late spring or early summer, select a nest site, and build a small paper nest in which they lay eggs. After eggs hatch from the 30 to 50 brood cells, the queen feeds the young larvae for about 18 to 20Â days. Larvae pupate, then emerge later as small, infertile females called workers. Workers in the colony take over caring for the larvae, feeding them with chewed up meat or fruit. By midsummer, the first adult workers emerge and assume the tasks of nest expansion, foraging for food, care of the queen and larvae, and colony defense.