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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 14Challenge 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.