PDA

View Full Version : A REAL math problem

axon
10-05-2003, 08:08 PM
Below you will find an interesting math problem. If there is enough interest, and no one will get the solution, I will post the solution in a few days. Hint: use imaginery numbers.

There is a treasure burried on a deserted island. Here are the instructions to the place where you can dig for the treasure. On one of the island's meadows on the north shore two trees stand; an ancient oak, and an ancient pine. There is also an old gallows. Start at the gallows and walk to the oak counting the steps. At the oak turn right by a right angle and take the same number of steps. Put a spike in the ground at this point. Now return to the gollows. Now walk to the pine and count the steps. At the pine turn left by a right angle and take the same number of steps. Put another spike here. Dig halfway between the spikes; the treasure is there.

You get to the island, but in time, the weather has destroyed the gallows; not even a trace of them is to be found. How do you find the treasure?

Silvercord
10-05-2003, 08:27 PM
get a real job so you don't have to go to deserted \$\$\$\$ing islands looking for buried \$\$\$\$ing treasure

axon
10-05-2003, 08:30 PM
Originally posted by Silvercord
get a real job so you don't have to go to deserted \$\$\$\$ing islands looking for buried \$\$\$\$ing treasure
I thought that this will be the response from some. It shows a lot from a "youth leader" like yourself silvercord. How about you try the problem, but if you find it borring/stupid, ot whatever, don't make any comments.

Silvercord
10-05-2003, 08:43 PM
:) I was just joking around, lol

I don't feel like trying the problem.

EDIT: besides, Ive got to lead our nation's youth to getting real jobs :)

haha

ZerOrDie
10-05-2003, 08:53 PM
My first year calculus professor did exactly the same problem :D I will refrain from answering ;)

axon
10-05-2003, 08:57 PM
Originally posted by ZerOrDie
My first year calculus professor did exactly the same problem :D I will refrain from answering ;)

Yet you don't need calculus to solve it!

confuted
10-05-2003, 09:02 PM
Originally posted by axon
Yet you don't need calculus to solve it!
You didn't need calculus for the problem my first year calc teacher gave us, either, but we sure tried it ;)

A man on a bike is 200 meters from a wall, traveling 10 meters per second toward the wall. There is a fly at the wall, which flies toward the bike at 1 meter per second. When it gets to the bike, it changes direction instantly and starts flying back toward the wall. When it reaches the wall, it changes direction instantly and starts flying back toward the bike. This continues until the fly is trapped between the bike tire and the wall and squished.

How far did the fly fly?

XSquared
10-05-2003, 09:16 PM
As the bike approaches the wall, the distance the fly travels approaches infinity.

confuted
10-05-2003, 09:21 PM
Originally posted by XSquared
As the bike approaches the wall, the distance the fly travels approaches infinity.
Absolutely not.

Zach L.
10-05-2003, 09:37 PM
I may be missing something, but the fact that the fly changes direction does not seem to matter.

The man will spend 20 s enroute, and at the fly's rate of travel, it will have moved a total of 20 m.

As for the other problem, still working on it.

JaWiB
10-05-2003, 09:39 PM
But wouldn't the fly hit the bike tire before he hits the wall? in 20 sec the bike hits the wall, in 20 seconds the fly is 20 meters away from the wall, so in 15 seconds the fly is at 185 and the bike is at 150 in 18 seconds the fly is at 182 and the bike is at 180 less than a second later the bike reaches the fly, at which point the fly turns around and the bike catches up with the fly and suddenly the fly is moving at 10 meters per second until BAM...so the answer is 36.2 meters since the fly made it exactly 18.1 meters before heading back 18.1 meters to meet his doom...

Zach L.
10-05-2003, 09:41 PM
Good point... Forgot the bike was moving faster than the fly.

Silvercord
10-06-2003, 05:31 AM
hey you guys you are forgetting axon's problem

XSquared
10-06-2003, 05:42 AM
I've already got that one figured out. Just not gonna post the solution yet.

DrZoidberg
10-06-2003, 06:10 AM
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.

axon
10-06-2003, 06:36 AM
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!

XSquared
10-06-2003, 12:49 PM
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.

*ClownPimp*
10-06-2003, 12:50 PM
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)

*ClownPimp*
10-06-2003, 01:03 PM
lol, now I see how you would use imaginary number (just replace imaginary numbers with 2d vectors)

axon
10-06-2003, 03:43 PM
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.

kermit
10-06-2003, 03:57 PM
Originally posted by axon
I thought that this will be the response from some. It shows a lot from a "youth leader" like yourself silvercord. How about you try the problem, but if you find it borring/stupid, ot whatever, don't make any comments.

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

axon
10-06-2003, 04:46 PM
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.

axon
10-06-2003, 04:47 PM
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.

kermit
10-06-2003, 04:56 PM
Originally posted by axon
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.

Actually, if I had known that the 'problem' had been flogged so hard on the board, I certainly never would have reposted it. I think next time I might just do a search on the board before I decide to post any similar such trivia - just to be sure that it hasn't been covered already.

axon
10-06-2003, 05:13 PM
Kermit: then I believe we have an understanding? cool...anyhow...try to get a solution to my problem...I'll post the solution soon.

kermit
10-06-2003, 05:33 PM
Ergh...so many problems...so little time - I have been working on cleaning up a program posted on the C board - its the currency conversion program where the guy thought he had problems with arrays - I can get it to compile now, and it 'works' but just a couple of stubborn little problems. Think I will post what I have done and someone else can take it from there...

Then maybe I will attempt your problem. :D

XSquared
10-06-2003, 07:27 PM
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.

XSquared
10-06-2003, 07:27 PM
Diagram:

*ClownPimp*
10-06-2003, 08:06 PM
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)

axon
10-07-2003, 06:40 AM
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:

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:

(.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/chem121/pics/island1.JPG