The requirement is not that clear

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    1. I don't quite understand the example. Why the game is over after I end up paying 21$ ? The fourth round I would be able to give the correct answer '8' (if I'm not stupid). Is it because that would not be counted strictly as a "guess" any more OR it is because I will be running out of my money?

    2. To "guarantee a win" , I have to assume the guesser is not that smart . i.e: he always picks the wrong number until he is able to guess the target correctly. E.g: for n =10 , and the target is 8, he would pick 1, 2,3,4,5,6,7, 10,9 , that sums to 47 already.

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