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When its two digits are interchanged number grows by > 36

This an example from my text book and it gives the answer as 17,19,27,29,39 and 49 but it doesn't give steps to solve. On other questions I have been able to determine the equation but I can't seem to solve with 2 variables.


Find all positive two digit odd numbers with this property: When the digits are interchanged, the result exceeds the original number by more than 36.

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This is not solved by means of an equation, but rather by logical study/classification of all the possible pairs of digits

Let us write a two-digit number as "ab", so that the one with digits interchanged is "ba"

It is required that ba - ab > 36

Obviously a > 0 as ab must be an honest two-digit, and b > a.

For definiteness, let us name cd = ba - ab, where c and d are digits as ...