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.
Please Explain
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?