Thread: A REAL math problem

Originally posted by DrZoidberg
If it is possible to find the treasure without knowing the position of the gallows that means it doesn't matter where the gallows was located. The outcome will be the same for all starting points. So just choose one. I suggest starting in the middle between the 2 trees.

you are correct, the starting position is rather arbitrary in this problem, but the solution is not as easy as you think. Different starting points will resultas in different amount of calculations to find the treasure. I suggest starting at the first quadrant. You can note that the relative position of the trees is arbitrary as well!

Start at the Oak, walk half of the distance to the other tree, turn left at a right angle, and then walk the same distance. Then you're at the treasure.

Its a fairly simple problem, although it may take a bit of calculation. Just use vectors. (Im too lazy right now to actually solve it, if no one else does it I will later)

lol, now I see how you would use imaginary number (just replace imaginary numbers with 2d vectors)

Originally posted by *ClownPimp*
lol, now I see how you would use imaginary number (just replace imaginary numbers with 2d vectors)

you're right ClownPimp, you could also use vectors; I even think that the solution might be more elegant this way. I will post the imaginery numbers solution later tonite.

Originally posted by kermit
hmmm...maybe the 'doctor' should have followed his own advice on the addition problem post...

I did start out my answer to your post with a rather rude comment, but that is because I've seen that done way too many times on these boards...not because I didn't lilke it. Therefore my comment was not directed at the problem, but at the post as a whole.

Originally posted by XSquared
Start at the Oak, walk half of the distance to the other tree, turn left at a right angle, and then walk the same distance. Then you're at the treasure.

what is your reasoning xsquared?

Kermit: then I believe we have an understanding? cool...anyhow...try to get a solution to my problem...I'll post the solution soon.

If the position of the gallows has no effect on the location of the treasure (T), then we can position the gallows (G) equidistant from the two trees (O and P), ans also so that OGP = 90 degrees. Therefore, if you do the construction, you will find that OGPT is a square, and that the two stakes are co-incident (same point). If you let the diagonal OP be 2, and label it's midpoint M, then OM=MP=1, and since it is a square, OP = GT, and therefore TM=MG=1. Thus, you just walk 1/2 OP from O, then turn left 90 degrees, and walk that same distance, and then start diggin.

Diagram:

See axon, you made it too simple by confirming that it didnt matter where the gallows was positioned. The real challenge is to show that it doesnt matter (ie, using an arbitrary starting position)

Yes, if I didn't say that the position of the gallows is arbitrary than the problem might have been a more tougher. Below is my solution, where the actual position of the gollows does cancel out.
Sorry about the ugly pic, but MSPaint is the only utility on this PC...
I haven't looked at your solution XSquared with any scrutiny yet, as time is of essence to me this morning....I will surely comment on it later tonite. Thanks to all who tried.

//solution:

consider the island as a plane of complex numbers; draw one axis (real)
throught the base of the two trees, and another axis (imaginery) at
right angles to the first, through a point half way between the trees.
Taking one half of the distance between the trees as our unit of
length, we can say that the oak is at the point -1 on the real axis and
the pine at +1. We don't know the location of the gollows so lets
call that position X.

Since we don't know where the gollows is we must consider X as a
complex number: X = a + bi

The seperation in distance and direction between X and the oak can be
denoted by (-1) - X = -(1+X). Similarly the separation between X and
the pine us 1 - X. To turn these two distances by right angles
clockwise and counterclocwise we must multiply them by -i and i, thus
finding the location where we must place our spikes:

Code:

      first spike:  (-i)[-(1+X)]+1 = i(X+1)-1
      second spike: (+i)(1-X)-1 = i(1-X)+1

Since the treasure is halfway between the pikes, we must now find
one half the sum of the two above comples numbers. We get:

Code:

      (.5)[i(X+1)+1+I(1-X)-1] = (.5)[+iX+i+1+i-iX-1]
                              = (.5)(+2i) = +i

So regardles of the position of the gollows we know that the treasure
must be located at +i. And +i is located at the intersection of the
imaginary axis with the line joining the two spikes, note the pic.

http://www.angelfire.lycos.com/linux...cs/island1.JPG