Brood X is Here! - The Solutions
05/17/2004

If we have the ratio 1.5 million / 1 acre and multiply that by 1 acre / 43,560 square feet (which is equivalent to multiplying by 1), we get 34.4 cicadas, to the nearest tenth.

In 17 years, there are 52 × 17 = 884 weeks. Only 2.5 of these weeks are spent above ground, which is 2.5 ÷ 884 = 0.3% of their lives!

We know that the 13-year cicadas will come out in 13, 26, 39, … years. These are multiples of 13. The 17-year cicadas will come out again in 17, 34, 51, … years, which are multiples of 17. We need to find the first number of years that is both a multiple of 13 and of 17. Since these numbers are relatively prime, the first multiple of both will be 13 × 17 = 221 years.

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