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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!
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?
Age 11 to 16
Challenge Level
Gabriel's Problem and Counting Factors might be good problems to try before looking at this one.
If you know the prime factors of a number, how can you work out which two-digit numbers are factors?
It might help to draw a factor tree.
If you'd like some help with the extension, click below
What is the largest that the four-digit number can be?
What is the smallest that the two-digit number can be?
What does this tell you about the three-digit number?
Now it might be helpful to think about the units digits.
NRICH is part of the family of activities in the Millennium Mathematics Project.