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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?

Chameleons

Age 11 to 14 Challenge Level:

On a certain island there are 12 green, 15 brown and 18 yellow chameleons. Whenever two chameleons of different colours meet they always change colour to the third colour (e.g. a brown and a yellow would both change to green when they met). This is the only time they change colour. Describe the shortest sequence of meetings in which all the chameleons change to green.

Now suppose there are 13 green, 15 brown and 17 yellow chameleons and they change colour in exactly the same circumstances. Is it possible now for all the chameleons eventually to be the same colour?