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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?

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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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Digit Sum

What is the sum of all the digits in all the integers from one to one million?

So Many Sums

Age 11 to 14 Short Challenge Level:

In this addition, each letter stands for a different digit, with $S$ standing for 3.

What is the value of $Y\times O$?




If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 



 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.