Here is a collection of interesting math problems. Despite appearances, they all have something in common. Can you figure out what it is?
- A single pair of baby rabbits is placed on an island. They take one month to grow up; after that, they have one new pair of baby rabbits every month. Each new pair of baby rabbits takes a month to grow up, then start having baby rabbits of their own, and so on. How many pairs of rabbits are on the island after n months?
- Susie can climb either one or two steps at a time. How many different ways can Susie climb a staircase with n stairs? (For example, she could climb a staircase of 3 stairs in 3 different ways: 1-2, 2-1, or 1-1-1.)
- How many different ways are there to tile a 2xn rectangle with 2×1 dominoes?
- If male bees (drones) are produced asexually from a female (queen), but female bees have two parents, one male and one female, how many ancestors does a male bee have in the nth generation before it?
Well, ok, I sort of gave it away with the tags…believe it or not, the solution to each problem is the Fibonacci numbers! For each problem, can you figure out why? Can you come up with your own problem which has the Fibonacci numbers as the solution?