Post your favorite math based riddles and puzzles here.
It's about time we had one of these threads.
My favorite one was actually posted on this forum awhile ago... had to do with tangents and circles... I'll see if I can find it.
Got it:
A space traveler named Rex is dropped off by his team at the bank of a river on a strange planet that has only one river. The river is completely straight and is very long. Rex begins to explore the planet in his dune buggy by driving in a straight line away from the river. But alas, his journey is abruptly ended when a tornado hits his dune buggy, spinning him around and knocking him unconscious so that he has forgotten which direction he was traveling.
Rex's dilemma: Rex does not know how to get back to the river so that his team can pick him up. What he does know is that he has traveled 1000 miles, he has enough gas in his tank to travel an additional 6400 miles. He has an accurate compass and an accurate odometer. He can travel in any direction he desires. What strategy should he employ to make sure that he can get back to the river?
(Any point on the river is OK)
Last edited by alkatran; Sep 25th, 2004 at 05:57 PM.
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Originally posted by dglienna look for the trees. vegatation needs water.
We had plenty of answers like that. It isn't that sort of problem, the answer is purely mathematical. Think of it as drawing a line which touches all the tangents of a circle.
Don't pay attention to this signature, it's contradictory.
Take a tree, reduce it to pulp using your phasers and then press it into paper, use tree sap to glue sand grains (from the river bottom) onto the paper and let it dry in the sun. Et voila, sandpaper.
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Walk in a circle with diameter 1000m
Not sure how you'd go about doing that. I guess every x metres walked you'd turn x/3140 * 360 degrees.... errrr..... ish. :S
You'd probably need sandpaper regardless.
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A space traveler named Rex is dropped off by his team at the bank of a river on a strange planet that has only one river. The river is completely straight and is very long. Rex begins to explore the planet in his dune buggy by driving in a straight line away from the river. But alas, his journey is abruptly ended when a tornado hits his dune buggy, spinning him around and knocking him unconscious so that he has forgotten which direction he was traveling.
Rex's dilemma: Rex does not know how to get back to the river so that his team can pick him up. What he does know is that he has traveled 1000 miles, he has enough gas in his tank to travel an additional 6400 miles. He has an accurate compass and an accurate odometer. He can travel in any direction he desires. What strategy should he employ to make sure that he can get back to the river?
(Any point on the river is OK)
Some Questions:
1.Where is the river located (around the central axis,east or west of the central axis and if so how far)?
2.(Joke)How can the river be straight and go around a circular planet (or is the planet flat)?
3.What is the radius of the planet?
4.What direction did he travel(east,west)(Does not matter if it is at the center)
5.I am assuming that the river goes all the way around the planet and if not then atleast far enough around that it looks circular(wraps around the planet)
But without those numbers I would do this:
1.Set up a marker and travel straight away from it in any direction.
2.Pray that another storm does not come.
3.Drive for 1066 miles and if i did not see the river turn back
4.Turn 120 degrees and do the same.
5. yo could do this 3 times for a little less than 6400 miles and if the plannet is the right size you may get lucky.
And if all else fails hit your com-badge and get them to beam you up.
The planet is so large that you might as well treat this problem as if he were on a flat plane. In fact, let's say the planet is flat.
He doesn't know which direction he travelled in (which is ironic, since he has a compass) and the river could be in ANY direction.
Travelling one direction, backtracking, then 90 degrees to that direction is only going to check 2 out of an infinite possible places for the river. (It's closest point could be at 45 degrees! He'd completely miss it!)
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by traveling the path of a 5-pointed star? 70 or so degrees so that he ends up back at the same place the he started if he doesn't find it? then south until he ran out of gas? he'd go about 1200 miles in each direction, and have 400 miles left.
Go 1000 miles any direction, then go in a circle with starting point as radius. Slightly better than 85% chance of seeing river...walk the rest?
Or
If he can see 123 miles into the distance...(using binoculars?)...drive 877 miles from start position then circle with start position as radius...always looking outwards...and you will find it.
(once you turn you must keep turning the same direction)
1.Go 1000 miles in any direction (this will get you to the rim of a 1000 mile circle)
2.Turn 90 degrees and go 1000 miles this will get you to one corner of a square that encloses the the 2000 mile diameter circle turn agian 90 degrees fro the direction you are traveling
3.Go 2000 miles in that direction.
4.Repeate the process until you run out of gas and you will find the river.
This will put you on a square path on the "Tangents of the circle" 4 sides each 2000 miles long you might say that that is 8000 total miles. but if the river is straight then it is also a tangent of your circle and you will find it before you go the 8000 miles I am guessing you will have some gass to spare if you pich the right direction to turn (if you pick right keep right if you pick left keep left)
(wouldn't have got it without twanvl's post though...ty)
It's almost the same, but instead of having sqrt 2 and 1 as the lines, you have them both the same to give the shortest distance. Using pythagoras this means that they are both sqrt 1.25 in length, to finish at a point 1000 miles from start point. Then do the semicircle as before and the straight line 1000 miles at the end, and you will definately find the river.
(Sorry I am no good at drawing)
Total distance covered = (2*(sqrt1.25) + pi + 1)*1000 miles
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