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Calendar Capers

Choose any three by three square of dates on a calendar page...

Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Winning Team

Age 11 to 14
Challenge Level

Nine cross country runners compete in a team competition in which there are three matches.

In the first match team X races against team Y, in the second it is team Y against team Z and in the third it is team Z against team X.

The runners are A, B, C, D, E, F, G, H and I and in all the matches, when they run, they finish in this order.

The teams are team X with runners A, F and H; team Y with runners B, D and I; and team Z with runners C, E and G.

In each match all the runners finish the course and 21 points are awarded, 6 points to the first, 5 to the second, 4 to the third and so on.

The judges work out the results of each of the three matches and try to decide on the winning team for the competition overall.

If you were a judge what would you decide and what is peculiar about the mathematics involved in this?