My 2 paisas

1. Fox and the holes

Posted on: November 18, 2010

This is another series of blogs I will be writing to archive all the good puzzles that I find. The reason behind this is that by blogging I will make sure that I understand not only the puzzle properly but also the way to find its solution. And the main cream in the puzzle is the simplicity of the technique through which u reach the solution and not the solution itself. So here is the Fox and the holes puzzle.

In a jungle, there are six holes in a line. A fox sleeps in one of these holes every night in such a way that it never sleeps in the same hole in two nights in a row. Also it always selects a hole right or left to the hole in which it slept the previous night. Now as a hunter, you have one chance every midnight to select any one and only one hole and catch the fox while he is sleeping. Device a strategy to find the minimum number of nights you will need to catch the fox.

Points to be noted: 1) If the fox is sleeping in the leftmost hole, then the next night he can sleep only in the hole right to it i.e. the second leftmost.
2) As mentioned, the fox will not sleep consecutively two nights in the same hole.

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