Cake plates

Put the plates in a triangle shape.

Put a different number of cakes on each plate, ranging from 1 cake to 6 cakes.

Make the numbers on each side of the triangle add up to 10.

Now do it so that each line of cakes adds up to 12

Age 11-14

Paving tiles

Mrs Tubbs bought some square paving tiles.

She bought less than 100 tiles, all the same size. She used all of them to pave two square areas of her garden.

Then she changed her mind.

She rearranged them all to make two different squares.

How many tiles did Mrs Tubbs buy?

SOLUTION

Paving tiles

Mrs Tubbs bought 50, 65 or 85 paving tiles. These are the only numbers less than 150 that can be expressed as the sum of two squares in two different ways.

50=52+52=72+12

65=72+42=82+12

85=62+72=22+92

What if Mrs Tubbs bought up to 150 tiles?

125=22+112=52+102

130=32+112=72+92

145=12+122 =82+92