Quandaries and Queries


Name: ebenezer

There are three digits. The middle digit is zero and the sum of the first and last digits are is 13. When the number is reversed it is increased by 297. What are the digits?



Hi Ebenezer,

The numbers look like X0Y and Y0X where X and Y are digits. One of them is 297 more than the other so the difference between them is 297. Write them down, one under the other, and think about the process of subtraction.

- Y0X

Since the middle digit of the answer is 9 and not 0 you must have borrowed when you subtracted X from Y to get the first digit of the answer. Thus to get the final digit of the answer (the digit 2) you subtracted Y from X-1. Hence X is 3 more than Y.

Thus what I see so far is

the sum of X and Y is 13, and

X is 3 more than Y
Hence adding Y and 3 and Y gives 13. What is Y?


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