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How Rabbits Multiply (illustration)
FILE No.169Unsolved

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?

Case Files

Diagram

Rabbit rulesItemDetailMonth 0One newborn pairBreedingFrom age 2 months, one pair each monthDeathsNoneHow many pairs at month 12?
Diagram

Hints

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.

Solve It

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.

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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.

Previous month + the one beforeMonth0123456Pairs11235813Month789101112Pairs21345589144233Month 12: 233 pairs.
Diagram of the solution

Key Points

  • Find the rule for how the number grows
  • It is the sum of the previous two
  • Write it out and check

Why people get fooled

Because you assume the number doubles every month.

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