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Three turtles are crawling along the straight road heading in the same direction. "Two other turtles are behind me",said the first turtle. "One turtle is behind me and one ahead", said the second. "Two turtles are ahead of me and one behind",says the third. How can this be possible?

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closed as off topic by Robert Israel, Austin Mohr, t.b., Ross Millikan, Gerry Myerson Aug 31 '12 at 3:28

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Perhaps the key is the turtles are crawling on some surface other than a flat plane. –  Austin Mohr Aug 31 '12 at 0:24
I am confused by the third turtle's statement. It seems as if there are four turtles –  SN77 Aug 31 '12 at 0:26
If the turtles were walking single file around a sphere, each turtle might be justified in saying that there are two turtles in front of him and two behind (referring to the same two turtles each time). Perhaps some other surface will fit your turtles' observations. –  Austin Mohr Aug 31 '12 at 0:39
I don't like this puzzle. –  Rahul Aug 31 '12 at 1:07
@RahulNarain Agreed, the puzzle is, in that case, very far from being mathematical. The "formalization" of the puzzle to give it a pseudo proof flavor is also distasteful. –  process91 Aug 31 '12 at 1:14

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