### 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!

### Multiplication Magic

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.

### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

##### Age 11 to 16 Challenge Level:

A mathematician goes into a supermarket and buys three items.

It has been a while since she has used a calculator and she multiplies the cost (in pounds, using the decimal point for the pence) instead of adding them.

At the checkout she says, "So that's £5.88" and the checkout attendant, correctly adding the items, agrees.

Can you find the values of the three items?

Once you've had a chance to think about the problem, you may like to look at Getting Started, where you can watch some video clips of Alison working on the problem.

I wonder if the same can happen with other values?
Alison wrote a computer program, and found three values that add together and multiply together to give £5.49.
Can you find them?

Alison's program also found three values that add together and multiply together to give £5.55. Can you find these?

You may wish to write a program of your own - if you do, we would love to hear about it. Remember, if you send us a solution to any of these problems, be sure to explain your thinking!

Extension

A mathematician goes into a supermarket and buys four items.

It has been a while since she has used a calculator and she multiplies the cost (in pounds, using the decimal point for the pence) instead of adding them.

At the checkout she says, "So that's £7.11" and the checkout attendent, correctly adding the items, agrees.

Find four possible prices of the items.

Very Challenging Extension: Prove that the costs giving rise to £7.11 are unique.

This problem has been adapted from the book "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education. This book is out of print but can still be found on Amazon.
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