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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.

Forwards Add Backwards

Age 11 to 14 Challenge Level:
 

The number $747$ can be formed by adding a $3$-digit number 
with its reversal: $621 + 126 = 747$, for example.

Can you find the other two ways of making $747$ in this way? 


Which other numbers between $700$ and $800$ can be formed from a number plus its reversal? 
There are more than five...

Can you explain how you know you have found all the possible numbers?


How many numbers between $300$ and $400$ can be formed from a number plus its reversal. And between $800$ and $900?$...

The number $1251$ can be formed by adding a $3$-digit number with its reversal.
Which other numbers between $1200$ and $1300$ can be formed from a number plus its reversal? And between $1900$ and $2000?$...



With thanks to Don Steward, whose ideas formed the basis of this problem.