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Mindreader

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

Score

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?

Chameleons

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12 green, 15 brown and 18 yellow chameleons.

Always the Same

Age 11 to 14 Challenge Level:

Arrange the numbers 1 to 16 into a 4 by 4 array.

Choose a number and circle it. Cross out the numbers which are in the same row and column as your chosen number.

Repeat this process twice more choosing from the remaining numbers.

This should leave you with one number remaining, circle this one also.

Add up your four circled numbers.

Why do they always add up to 34 whatever way you choose your numbers?