CombinatoricsDifficulty 5.1AIME, harderFind the answer
## 162. Math Puzzle 11/78
Assume that a fly lays 120 eggs at the beginning of summer, on June 21st, and after 20 days, fully developed insects emerge from these eggs, each of which then lays 120 eggs. How many "descendants" would this fly have in total by the beginning of autumn?
A number or a short expression. Spacing and $ signs are ignored.
Solution
Summer lasts 95 days. During this time, four generations of flies can lay their eggs:
June 21
1 fly
after 20 days
120 flies
after 40 days
14400 flies
after 60 days
1728000 flies
after 80 days
207360000 flies
Total
209102520 flies
By the beginning of autumn, on September 23, the fly would theoretically have more than 209 million offspring.
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