Three turtles are lined up in a row. The first turtle said, "I've got 2 turtles behind me and no turtles in front of me." The second turtle said: "I've got 1 turtle behind me and 1 turtle in front of me." but the last turtle surprised the other two and said, "I've got 2 turtles behind me and 2 turtles in front of me."

How is that possible?

The turtles do not say the other turtles they see are directly in front of or behind them.  They simple tell us about all the turtle that were not directly to there left or right.  Let's say the line they are on runs north and south.  The first turtle faces due north and count the 2 turtles behind him.  He does not count the two turtles due east of him because they are nether in front of nor behind him.  

The second turtle is due south of the first and is facing north by north east.  The two unnamed turtles east of the line of three consist of a small turtle sitting on top of a large turtle so that they are both directly left of the second turtle.  The second turtle sees only turtle one as being in front of him and turtle three as being behind him.  

The Third turtle is due south of the first two and is facing east by north east. He faces so far east that the stacked turtles are behind him. He does not, however, face due east so turtles one and two are in front of him.

Furthermore, Because the number of turtle in front of and behind turtle three are equal, turtle three could be facing in the opposite direction.  Also, Turtle one could face due east counting the stacked turtles while ignoring turtles two and three directly to his right.

Posted by Axorion on 2007-11-18 05:59:23