The difference between a two-digit number and that number reversed is 18. What could the number be? List all the possibilities

9514 1404 393

  31, 42, 53, 64, 75, 86, 97

Step-by-step explanation:

The difference when the digits are reversed is 9 times the difference between the digits. The largest of the two numbers has tens digit n, and ones digit n-2, for n in {3, 4, 5, 6, 7, 8, 9}.

The possible numbers are ...

  31, 42, 53, 64, 75, 86, 97

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Consider number to, where 't' is the tens digit, and 'o' is the ones digit. Then the difference in values between that number and its reverse is ...

  (10t +o) -(10o +t) = 9(t -o)

We want that difference to be 18, so ...

  9(t -o) = 18

  t - o = 2

Since we want the numbers to be 2-digit, the numbers 20 and 02 are ruled out. That is, 9 ≥ t ≥ 3, and 7 ≥ o ≥ 1.