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In order to answer this question we have to make the assumption that none of the drones and queens share a parent otherwise the figures will become impossible to calculate. Bear in mind that each queen will mate with up to 20 drones, although each drone will only mate with one queen because it will die after mating.
The figures below are worked on the basis that each queen has two parents (a queen and a drone) and each drone only has one (the queen):
* Generation 1: 1 queen * Generation 2: 1 queen, 1 drone * Generation 3: 2 queens, 1 drone (mothers of the queen and drone, father of the queen) * Generation 4: 3 queens, 2 drones * Generation 5: 5 queens, 3 drones * Generation 6: 8 queens, 5 drones * Generation 7: 13 queens, 8 drones * Generation 8: 21 queens, 13 drones * Generation 9: 34 queens, 21 drones * Generation 10: 55 queens, 34 drones This gives a grand total of 143 queens and 88 drones.
Those of a mathematical persuasion will notice that this is a perfect example of a Fibonnacci sequence, both for the numbers of queens and the numbers of drones.
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