Comments on: Yoak: Pirate Treasure Map

By: The Pirate’s Treasure « Where the Arts Meet the Sciences

The Pirate’s Treasure « Where the Arts Meet the Sciences — Thu, 10 May 2012 22:44:55 +0000

[…] on-line versions of it (physicsforums.com, mathpages.com, Bradley University, geometer.org, the mathfactor podcast, and University of Georgia), I couldn’t remember how I had solved it! It apparently appears […]

By: jyoak

jyoak — Tue, 24 Jan 2012 22:42:31 +0000

Jeremy, that's part of the statement of the problem. It is the last sentence in the second paragraph.

By: Jeremy

Jeremy — Tue, 24 Jan 2012 22:19:00 +0000

Can someone explain why the treasure is always the midpoint between the two flags?

By: Sue VanHattum

Sue VanHattum — Fri, 31 Dec 2010 14:50:56 +0000

My first comment makes me think I had a solution when I wrote it. But I now have no idea what my solution was. Oh well, that allows me the pleasure of solving it again. But my efforts this time don’t give me any elegant answers…

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.

By: Ron

Ron — Wed, 24 Feb 2010 16:17:15 +0000

Yep ! I found the Gamow book I told you about on line w/ ability to go in and read some pages– and the problem and solution using imaginary numbers is around pages 35-37
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!!

By: Byon

Byon — Wed, 24 Feb 2010 03:07:36 +0000

Thanks, Jeff. Yes, I guess you could also consider a different square where the trees mark opposite corners, and the treasure is one of the remaining corners. But I saw it as a square sqrt(2) larger than that, where the trees marked adjacent corners, and the treasure was in the center of that square. Both should work. Thanks again for the fun problem!

By: Stephen Morris

Stephen Morris — Tue, 23 Feb 2010 20:23:26 +0000

Just checked, yes you can do it with complex numbers.

By: jyoak

jyoak — Tue, 23 Feb 2010 19:30:52 +0000

Ron,

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.

By: Ron

Ron — Tue, 23 Feb 2010 16:12:14 +0000

Is this the same (or simlilar ) to aproblem in George Gamow’s book One two three…..Infinity ? He used (as I recall–don’ have the book any more) complex numbers to solve it>

By: Sean McCloskey

Sean McCloskey — Mon, 22 Feb 2010 19:01:53 +0000

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).