Magic 1089

October 3, 2014

I’ve been very busy at work this week, so I only have time for a simple exercise today.

This is a simple puzzle in arithmetic. Take any three-digit number with digits in descending order; for instance, 532 is acceptable, but 481 is not. Reverse the digits of the original number, and subtract the reversal from the original. Then reverse that difference, and add the reversal of the difference to the difference. Write the result as output.

For instance, start with the number 532. Its reversal is 235, and the difference is 532 – 235 = 297. Reversing the difference gives 792, and 297 + 792 = 1089, which is the result.

Your task is to write a program that makes this calculation, and try it on several different starting numbers; you might enjoy working out the arithmetic behind the results that you see. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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