Just Repeat
Just repeat!
Think of any three-digit number.
Repeat the digits
e.g.
234 ....... 234 234
973 ...... 973 973
Both 6-digit numbers are divisible by 91.
Is this a coincidence?
Are there other patterns and connections?
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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.