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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!

Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

The Genie in the Jar

Age 11 to 14 Challenge Level:

Why do this problem?

This problem requires both clear thinking and the use of prime factors. It does not require much knowledge of volume and capacity.

Key questions

What are the factors of $595$?
What is its most obvious factor?
Why not try dividing by $5$?
What are the factors of the result of doing this?
Why not call the "numbers" g, o and v?
Does the problem ask which number is which?

Possible extension

Learners could go on to Stars for more work on factors.

Possible support

Suggest doing Three Spinners which is a simpler problem involving factors.