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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?

Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Add to 200

Age 11 to 14 Challenge Level:

Choose any four digits (from 0, 1, 2, ... , 9) and place them in the cells below (you can repeat digits).

 
Read the two 2-digit numbers across and add them together.
Read the two 2-digit numbers down and add them too.
Then add these two totals together.

For example:
             

Try a few examples of your own.

Is there a quick way to tell if the total is going to be even or odd?

Can you make a total of 200? 
How many ways are there of doing this?

If we use four 0s, the total would be 0.
If we use four 9s, the total would be 396.
Which numbers between 0 and 396 is it possible to make?


With thanks to Don Steward, whose ideas formed the basis of this problem.