Age 7-11. Making chains

The blacksmith has lots of small pieces of chain, each with four links. To make longer chains, he cuts a link, joins pieces, then welds the cut.

He charges 10p to cut a link and 20p to weld it.

Harry wants a chain with 24 links. The blacksmith says it will cost Pounds 1.80. Harry says it should cost only pound;1.20. How does Harry think the chain should be made?

Age 11-14

Lunch party

Seven friends are having lunch in the same cafe.

The first eats there every day, the second every other day, the third every third day, the fourth every fourth day, the fifth every fifth day, the sixth every sixth day, and the seventh once a week on the same day.

The next time they all meet at the cafe they are planning to have a lunch party. In how many days from now will the party be?

SOLUTIONS Making chains: The chain can be made by taking 6 small pieces of chain, each with 4 links. Cut one piece into 4 individual links and use these to join the other 5 pieces. Total cost: 30p x 4 = pound;1.20.

Lunch party: 420 days from now, since 420 is the lowest common multiple of 1, 2, 3, 4, 5, 6 and 7.