Okay, here's an interesting problem. (Well, *I* think it's interesting!)
On an island, there are a gallows, an oak tree, and a palm tree. Your treasure map gives the following directions: Start at the gallows. Walk to the palm tree, counting the number of steps. Turn left 90 degress, then walk the same number of steps. Mark your position with a stake and go back to the gallows.
Now walk to the oak tree, counting the number of steps. Turn right 90 degrees and wald the same number of steps. Mark your position with a stake.
Now find the midpoint of the segment formed by the two stakes. Dig there and you will find the treasure.
You arrive at the island, and the gallows are gone. Can you still find the treasure?? How??
-- -- Michelle Manes Reasearch Assistant, Connected Geometry Project Education Development Center