Apples and Banana
Ninety-eight apples who always lie and one banana who always tells the truth are randomly arranged along a line. The first fruit says “One of the first forty fruit is the banana!” The last fruit responds “No, one of the last forty fruit is the banana!” The fruit in the middle yells “I’m the banana!” In how many positions could the banana be?
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1 solution
The first statement implies that the first one is the banana or none of the first 40. The second statement implies that the last one is the banana or none of the first 40. The last statement provides no information since anyone could have said it.
So the banana could be the first, last or any of the middle 19.