Overview
Fibonacci introduced this sequence in 1202 to model idealised rabbit breeding. It reappears in sunflowers, pinecones, and the golden ratio.
How to solve Fibonacci's Rabbits
- Each month's mature pairs equal last month's total (they all survive).
- New pairs equal the count two months ago (only mature pairs breed).
- So each term is the sum of the previous two: 8 + 13 = 21.
The key insight
A one-month maturation delay is exactly what makes 'add the previous two' the right rule — the delay reaches back one extra step.
Variations & echoes
- Ratios of consecutive terms converge to the golden ratio φ ≈ 1.618.
- Fibonacci numbers count many things, from stair-climbing paths to tilings.
Frequently asked questions
Does it start at 0 or 1?
Both conventions exist; the rabbit story starts 1, 1, 2, 3, … while the mathematical definition often begins 0, 1, 1, 2, ….