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### Number and algebra

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### Working mathematically

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### For younger learners

# Dicing with Numbers

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### Adding All Nine

### Summing Consecutive Numbers

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Age 11 to 14

Challenge Level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

What can you say about rows of four, five, six, ...... dice?

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!

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?