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The Drunken Warden?
A jail consists of 100 cells in a line, all starting out closed. The warden gets drunk one night and goes along opening every single cell. He then returns to the beginning, and "toggles" every second cell -- in this case, they're all open, so he closes every other cell door. He then runs to the beginning again, and "toggles" every third cell, then again with every fourth cell, and so on until the very last run in which he only toggles the hundredth cell, then drops down from exhaustion.
How many cells are left open after this process?
6 Answers
- 2 decades agoFavorite Answer
10. Ten. Every cell that is a perfect square will remain open
(1, 4, 9, 16, 25, 36, 49, 64, 81, and 100). If a number is not
a perfect square, then it has an even number of divisors,
therefore it will be "toggled" an even number of times and
end up where it started (closed). Perfect squares have an odd
number of divisors, so they will end up the opposite of where
they started (open).
- 2 decades ago
1. He never toggled the first cell.
Source(s): my brain (after coffee) - Anonymous2 decades ago
2 like in 2pts
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