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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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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.