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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!

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Have You Got It?

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

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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:

How many integers between 1 and 1200 are multiples of 2?

How many integers between 1 and 1200 are multiples of 3?

How many integers between 1 and 1200 are multiples of 5?

Some integers are multiples of both 2 and 3, of both 2 and 5, of both 3 and 5...

Some integers are multiples of 2, 3 and 5...

Can the Venn diagram in the question help, if you consider that the multiples of 2, 3 and 5 each correspond to one of the sets (circles)?