Describing patterns and sequences

problem
Favourite

Attractive Tablecloths

Age

14 to 16

Challenge level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem

Counter Ideas

Age

7 to 11

Challenge level

Here are some ideas to try in the classroom for using counters to investigate number patterns.
problem

Taking Steps

Age

7 to 11

Challenge level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
problem

Triangular Hexagons

Age

7 to 11

Challenge level

Investigate these hexagons drawn from different sized equilateral triangles.
problem

Mobile Numbers

Age

5 to 11

Challenge level

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
problem

Mean Sequence

Age

11 to 14

Challenge level

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?
problem

Expanding Pattern

Age

11 to 14

Challenge level

How many squares are needed to continue this pattern?
problem

Paving Paths

Age

11 to 14

Challenge level

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?
problem

Archimedes and Numerical Roots

Age

14 to 16

Challenge level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem

Lastly - Well

Age

11 to 14

Challenge level

What are the last two digits of 2^(2^2003)?