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 bee When conditions are favorable for swarming, the queen will start laying eggs in queen cups. A virgin queen will develop from a fertilized egg. The young queen larva develops differently because it is more heavily fed royal jelly, a protein-rich secretion from glands on the heads of young workers. If not for being heavily fed royal jelly, the queen larva would have developed into a regular worker bee. All bee larvae are fed some royal jelly for the first few days after hatching but only queen larvae are fed on it exclusively. As a result of the difference in diet, the queen will develop into a sexually mature female, unlike the worker bees.