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Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

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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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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

What Numbers Can We Make Now?

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

This problem follows on from What Numbers Can We Make?

 

The interactivity below creates sets of bags similar to those in What Numbers Can We Make?

Investigate what numbers you can make when you choose three numbers from the bags. Once you think you know what is special about the numbers you can check your answer.

You can also find what is special when you choose four, five or six numbers.

When you have an efficient strategy, test it by choosing 99 or 100 numbers.

Always enter the biggest possible multiple. The "plus" number may include zero.

 

Choose numbers from the bags and find their total.

The answer is always than a multiple of


Can you explain your strategies?
 
And finally...
 
If the bags contained 3s, 7s, 11s and 15s, can you describe a quick way to check whether it is possible to choose 30 numbers that will add up to 412?

 
There are a few related problems that you might like to try:

Shifting Times Tables
Charlie's Delightful Machine
A Little Light Thinking
Remainders
Where Can We Visit?
Cinema Problem