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I think you're missing the cases when you have 12343 and you have to append 21 or
- erikseulean December 27, 2015123432 and have to append only 1.
My solution would be to find the middle and try to check left and right until there's a missmatch. If I find a missmatch, it means the middle is incorrect so I increment it with 1 till I find the correct middle (both to the left and right I have the same values) or I hit the end (when none of the values match).