What is the smallest number, besides 1, that is one less than twice its digits reversed ?



Answers:
73

The next one I think is 793
Let t = the original tens digit and o = the original ones digit.

Then the original number is 10t + o.

The digits reversed would be 10o + t.

So 10t + o + 1 = 2(10o + t).

10t + o + 1 = 20o + 2t

19o = 8t + 1

Then you just pick sample values of o, and solve for t, looking for integer answers.

19(0) doesn't work
19(1) = 8t + 1 -> 8t = 18, no dice
19(2) = 8t + 1 -> 8t = 37, no dice
19(3) = 8t + 1 -> 8t = 56, so t = 7

Therefore the number is 73.
73
2 x 37 = 74
It is 73

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