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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!

Have You Got It?

Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Inclusion Exclusion

Age 11 to 14
Challenge Level

Since this problem can be tackled in a variety of ways it can lead to useful discussions on the merits of different strategies.

If students disagree about the correct answer they can be challenged to develop convincing arguments that justify their conclusions.