Correct solutions were also received from Felice Kelly, and from Bradley alumnus Brian Laughlin, as well as from Robert T. McQuaid, B Dunne, and Jack Wang. 

The solution can be read off the diagram below, as submitted by Ray Kremer.

Since the pirates turned at a 90 degree angle, the two green triangles are equivalent as are the two blue triangles.  This allows us to find the final coordinates of the pirates.  It's now an easy task to determine that the midpoint of the line joining the pirates' final positions has coordinates (50,50), and is, in fact, independent of the location of the tree!

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