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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.
Big Powers
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.
Age 11 to 14 Challenge Level:
Take a look at the two multiplications below. What do you notice?
$32 \times 46 = 1472$
$23 \times 64 = 1472$
The digits in this multiplication have been reversed, and the answer has stayed the same!
Is this surprising? Can you find other examples where this happens?
What do you notice about the pairs of two digit numbers that produce this special result?
NRICH is part of the family of activities in the Millennium Mathematics Project.