Fibonacci sequence

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

You add 1 to the golden ratio to get its square. How do you find higher powers?

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

What have Fibonacci numbers got to do with Pythagorean triples?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.