Patterns and Sequences: Age 14-16

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.

problem
Favourite

A Little Light Thinking

Age

14 to 16

Challenge level

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
problem
Favourite

Steel Cables

Age

14 to 16

Challenge level

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Favourite

Double Trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
problem
Favourite

Picture Story

Age

14 to 16

Challenge level

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
problem
Favourite

Painted Cube

Age

14 to 16

Challenge level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
problem
Favourite

Mystic Rose

Age

14 to 16

Challenge level

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Favourite

Partly Painted Cube

Age

14 to 16

Challenge level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?