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# Add to 200

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### Double Digit

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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.*

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?

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.

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.