# Brainteasers

All square

How many squares can you count in this diagram?

Tug-of-war

Mr and Mrs Jones have two pairs of identical twins, Ann and Alison, and John and James. They all took part in a tug-of-war competition at a village fete.

The two boys and a girl beat their father.

The two girls and a boy lost to their mother.

One of the girls and their father then played one of the boys and their mother.

Who do you think won?

SOLUTIONS All square (ages 6 to 12): There are 31 squares in the diagram: seventeen 1 by 1, eight 2 by 2, five 3 by 3, and one 5 by 5. Tug-of-war (ages 10 to 14): The mother and boy team won. The problem can be solved by constructing and solving some simple inequalities: 2B + G

F, so B + G

F - B; 2G + B

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