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problem

Holly

14 to 16

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.

problem

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?

problem

Escriptions

16 to 18

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

problem

Square pizza

14 to 16

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

problem

Difference

7 to 11

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

problem

Brailler

11 to 14

The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?

problem

Flow chart

11 to 14

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

problem

Right angle challenge

5 to 7

How many right angles can you make using two sticks?

problem

Prize pony

14 to 16

When Helen moved her favourite pony from one stable to another, the average value of the horses in each stable increased by £10000. What is the total value of all the ponies?

problem

Split clock face

11 to 14

Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.

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Holly

How many dice?

Escriptions

Square pizza

Difference

Brailler

Flow chart

Right angle challenge

Prize pony

Split clock face