Hidden Treasure

A band of pirates buried their treasure on an island. They chose a spot to bury it in the following manner. Along the shore, there were two large rocks about 100 feet apart. Somewhere between the rocks and about 80 feet from the shore was a large palm tree. Two pirates, one standing on each rock, faced the palm tree, turned 90 degrees away from the palm tree and walked inland a distance equal to that between their rock and the palm tree. The other pirates buried the treasure at the point midway between where the pirates ended up.
Years later these directions came to light and a party of wealthy adventurers sailed off to find the treasure. When they reached the island, they found the large rocks with no trouble but the palm tree was long gone, probably as a result of a hurricane. Deciding it was hopeless, all went home, except for the cabin boy who decided to stay for a while. Once alone, he immediately walked to the exact spot of the buried treasure and dug up his fortune.
How did he know the location of the treasure?


Answer:

Please click the link for the diagram.
http://bradley.bradley.edu/~delgado/images/s43.gif

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!