Fibonacci sequence

problem

Golden Fractions

Age

16 to 18

Challenge level

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

Room Doubling

Age

7 to 11

Challenge level

Investigate the different ways you could split up these rooms so that you have double the number.
problem

Colour Building

Age

11 to 14

Challenge level

Using only the red and white rods, how many different ways are there to make up the other rods?
problem

Fibonacci Deduction

Age

11 to 14

Challenge level

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

Logo Challenge - Circles as Bugs

Age

11 to 16

Challenge level

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.
problem

First Forward Into Logo 11: Sequences

Age

11 to 18

Challenge level

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
game

Last Biscuit

Age

11 to 18

Challenge level

Can you find a strategy that ensures you get to take the last biscuit in this game?
problem

Building Gnomons

Age

14 to 16

Challenge level

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
problem

Gnomon Dimensions

Age

14 to 16

Challenge level

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
problem

Ordered Sums

Age

14 to 16

Challenge level

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate a(n) and b(n) for n<8. What do you notice about these sequences? (ii) Find a relation between a(p) and b(q). (iii) Prove your conjectures.