How Rabbits Multiply

Difficulty ★★☆about 5 minLogic PuzzleRecurrencesFibonacci

A newborn pair produces a new pair every month starting at age two months. How many pairs after 12 months?

Case Record

There is one pair of newborn rabbits. Rabbits produce one pair of young every month, starting two months after birth. No rabbits die.

Your question

Taking now as month 0, how many pairs will there be in total at month 12?

If you get stuck, open the hints one at a time, in order.

Open hint 1

Can a newborn pair have young?

Open hint 2

This month's number = last month's number + ?

Open hint 3

Write out month 1, month 2, month 3, and so on.

Your question

Taking now as month 0, how many pairs will there be in total at month 12?

Choose the answer closest to the truth.

233 pairs

The answer is "233 pairs."

The number of pairs is the sum of the previous month and the month before that: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 (at month 12).

4,096 is the value if the number doubled every month. Rabbits start to give birth only after two months, so that is not the case.

Diagram of the solution

Because you assume the number doubles every month.

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