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### Advanced mathematics

# Patterns and Sequences - Stage 4

### Picture Story

### Attractive Tablecloths

### Painted Cube

### Mystic Rose

### Slick Summing

### Partly Painted Cube

### A Little Light Thinking

### Steel Cables

### Patterns and Sequences - Short Problems

### Diagonals

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Age 14 to 16

Challenge Level

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

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?

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?

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.

Age 14 to 16

Challenge Level

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

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?

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?

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?

Age 11 to 16

A collection of short problems on patterns and sequences.

Age 14 to 16

ShortChallenge Level

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