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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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Ewa's Eggs

Age 11 to 14 Challenge Level:

Why do this problem?
This problem challenges learners to think about multiples and may lead to interesting discussions and insights about common multiples and lowest common multiples.

Possible approach
If the learners can't get started discuss with the class how they might change the problem to make it simpler, solve the simpler problem and then go back to the original problem.

Key questions
To use this approach:

The problem says the eggs could have been divided into piles in five different ways, with 2, 3, 4, 5 or 6 eggs in each pile and one left over, can you make up a problem and solve it where the eggs could be divided into piles in JUST TWO different ways?

Can you draw some quick diagrams of the different arrangements into piles using dots for the eggs?

What did you do to solve your simple problem? Can you use the same method for the problem with 5 piles?

If not can you make up and solve a problem with 3 piles?

Possible extension
Try LCM Sudoko or Take Three from Five

Possible support
Start with Make 37