One hundred people numbered 1 to 100 stand in a circle. Person 1 holds a sword and eliminates Person 2, passing the sword to Person 3. Person 3 eliminates Person 4 and passes to Person 5. This pattern continues in order around the circle until only one survivor remains. What is the number of the last survivor?
73
This is the Josephus Problem with step size 2. The formula for the survivor position is 2(N - 2^k) + 1, where 2^k is the largest power of 2 less than or equal to N. For N = 100, 2^k = 64. Thus, 2(100 - 64) + 1 = 2(36) + 1 = 73.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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