7th October 2005 at 01:00
All square

How many squares can you count in this diagram?


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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