Patterns and Sequences - Stage 4

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?

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?

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?

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.

Slick Summing

Age 14 to 16
Challenge Level

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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?

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?

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?

Double Trouble

Age 14 to 16
Challenge Level

Simple additions can lead to intriguing results...

Patterns and Sequences - Short Problems

Age 11 to 16

A collection of short problems on patterns and sequences.

Diagonals

Age 14 to 16 Short
Challenge Level

How many diagonals does a regular icosagon (20 sides) have?

Difference Sequence

Age 14 to 16 Short
Challenge Level

When will 2000 appear in this sequence?