I’m writing to point out that all of our ideas seem to allow for two different possible locations for the treasure. Perhaps one of those locations was in the water, so the pirate knew to dig at the other.

]]>One could also use vector algebra could we not?

I enjoy the MAA site very much. I am a 76 year old retired high school math teacher who tries to keep my brain from going dead!! ]]>

I’ve never seen that book, but it sure does look interesting. Thanks for the pointer.

I got the inspiration for this puzzle, if I remember correctly, from the IBM site Ponder This which can be found here: http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/pages/index.html . I’m not sure how literally I took it nor am I even 100% sure this is where I got it, but regardless it is an interesting source of puzzles.

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I have a slightly different version of Byon’s solution, which was easier for me, though it might be more complicated to some.

Assume a coordinate plane centered at the large tree, with the x-axis passing through both trees. Your coordinates from any arbitrary point on the island are (a,b). The function f(a,b) –> (-b,a) maps to your destination after following the first set of instructions.

Now go back to your starting point (a,b) and assume a coordinate plane centered on the smaller tree. Your coordinates with respect to this new origin are (a-x, b), where x is the distance between the two trees going in the direction from the larger tree to the smaller tree. The function g(a,b) –> (b,-a) describes your destination after following the second set of instructions, so you arrive at (b, -a+x). But this is relative to the small tree. Relative to the large tree your second destination is (b+x, -a+x).

All that’s left to do is find the midpoint between (-b,a) and (b +x ,-a+x). So the midpoint is (x/2 , x/2).

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