A New Doomsday Clock

Discrete Mathematics Level 2

If rabbits suddenly became immortal, invincible, and if they matured and reproduced independently of their environment, about how long would it take until rabbits literally covered the earth?

Helpful (but also somewhat disturbing) facts:
- The earth has about \(5 \times 10^{14}\) square meters of surface area.
- Approximately 20 rabbits can fit in one square meter.

  • Rabbit litters range from 1-14 babies. 6 is a conservative average.
  • Rabbits can begin reproducing when they're about 6 months old.
  • Rabbit gestation lasts about one month.
  • Rabbits are "induced ovulators" and can be impregnated again within minutes of giving birth.
  • There are probably around \(10^{9}\) rabbits currently alive.


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