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There are **30** NRICH Mathematical resources connected to **Fibonacci sequence**, you may find related items under Patterns, sequences and structure.

Problem
Primary curriculum
Secondary curriculum
### Fibonacci Surprises

Play around with the Fibonacci sequence and discover some surprising results!

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 1 Step 2 Step

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fibs

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Farey Fibonacci

Investigate Farey sequences of ratios of Fibonacci numbers.

Age 16 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Building Gnomons

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Simple Train Journeys

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### First Forward Into Logo 11: Sequences

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

Age 11 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Whirling Fibonacci Squares

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Colour Building

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plus or Minus

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pythagorean Fibs

What have Fibonacci numbers got to do with Pythagorean triples?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fibonacci Fashion

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Golden Mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### The Golden Ratio, Fibonacci Numbers and Continued Fractions.

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

Age 14 to 16

Problem
Primary curriculum
Secondary curriculum
### Golden Fractions

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sheep Talk

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?

Age 7 to 11

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Last Biscuit

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

Age 11 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Leonardo of Pisa and the Golden Rectangle

Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.

Age 7 to 16

Article
Primary curriculum
Secondary curriculum
### Fibonacci's Three Wishes 2

Second of two articles about Fibonacci, written for students.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Golden Fibs

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fibonacci Factors

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ordered Sums

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stringing it Out

Explore the transformations and comment on what you find.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge - Circles as Bugs

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

Age 11 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Continued Fractions I

An article introducing continued fractions with some simple puzzles for the reader.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Gnomon Dimensions

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Paving Paths

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Powers

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Room Doubling

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

Age 7 to 11

Challenge Level