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?

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.*

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 $2000?$...