the argument i hear about induction is that it's only valid IF n=1 is a true situation, n=2 is a true situation, etc, up to n=k (where k is 100 here). But we are only given n=100, and we cannot say that n=1,2,3... is true. The best counter example is the surprise execution paradox: suppose you are a prisoner, about to be executed next week. However, a strange rule applies - if you are not surprised by the date of your execution, you get to go free. You reason that you cannot be executed on sunday, the last day, since by friday, you'd know, and thus not be surprised. by induction, friday is also not a possible day, since you'd know by thurs, etc. You conclude that you cannot be surprised, and this will not get executed. But come wed, you get executed, and is completely surprised!