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# Forwards Add Backwards

The number $747$ can be formed by adding a $3$-digit number
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Age 11 to 14

Challenge Level

*Forwards Add Backwards printable worksheet*

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.*

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.