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Topic: Crossing water canal (Read 1277 times) |
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scuder
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Crossing water canal
« on: Jan 12th, 2005, 5:10am » |
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A rectangular island of 50x70 meters dimensions is surrounded by a water canal of 10 metres width. You have two wooden planks each 7 meters in length, how will you enter the island without entering the water.
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TenaliRaman
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Re: Crossing water canal
« Reply #1 on: Jan 12th, 2005, 6:54am » |
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What are the restrictions?
Two 7 meter planks can be attached together quite rigidly to get something of length of 12 which should solve the problem.
-- AI
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ThudnBlunder
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Quote:| Two 7 meter planks can be attached together quite rigidly to get something of length of 12 |
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If that were allowed it wouldn't be much of a puzzle, would it?
In fact, this is an oldie - dating from 1879, according to my former supervisor (who has written a chronology of recreational mathematics). See diagram below for the usual method.
Let width of canal = W
Let lengths of planks = X and Y, where X [smiley=geqslant.gif] Y
Then the canal can in theory be bridged if
X + Y/2 > [smiley=surd.gif]2 * W
If X = Y, we must have X/W > (2[smiley=surd.gif]2)/3 = 0.94281...
But we are given that X/W = 0.7
So, either the width of the canal is wrong, and/or the length of at least one plank is wrong, or this method is wrong. (My money is on the first. However, why are the dimensions of the island given? Must be a red herring, eh?)
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| « Last Edit: Jan 13th, 2005, 2:59am by ThudnBlunder » |
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TenaliRaman
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Re: Crossing water canal
« Reply #3 on: Jan 12th, 2005, 8:09am » |
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Ah indeed!
But since no restrictions were mentioned i just assumed the easiest answer!!
My money is on the first one too then 
-- AI
P.S -> Maybe its not a rectangle. Its possible maybe if it were a rhombus? Just speculating.
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| « Last Edit: Jan 12th, 2005, 8:17am by TenaliRaman » |
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Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
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rmsgrey
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Re: Crossing water canal
« Reply #4 on: Jan 12th, 2005, 8:30am » |
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What happens when the corners are rounded? It doesn't seem to help in this case, but it should affect the critical lengths.
And what's the width of the planks?
For that matter, what's the bouyancy like?
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Grimbal
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Re: Crossing water canal
« Reply #5 on: Jan 12th, 2005, 10:04am » |
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And when there are 2 persons, there is another solution.
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scuder
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Re: Crossing water canal
« Reply #6 on: Jan 12th, 2005, 10:01pm » |
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I also tried the same way as THUDandBLUNDER did. This was a Microsoft Puzzle. I found a similiar puzzle in one of the sites:
King Just is growing old. He has no children, and has decided to leave his vast tropical kingdom to the person who can solve this problem. He has a pool dug, 30 feet square and 15 feet deep. In the center is a platform 10 feet square, and level with the sides of the pool. The walls are smooth and vertical. The water in the pool is 12 feet deep. On the platform he has placed his royal scepter (which is gold and weighs 30 pounds). In the pool he has placed a dozen hungry sharks.
The person who can retrieve the scepter and hand it to the king will inherit the kingdom. To do that you are given 2 wooden planks. Each plank is 8 feet long, 1 foot wide, 2 inches thick and weighs 40 pounds. You are not allowed to join the planks together (such as with nails, glue, or rope). You are given only 1 minute for the task.
How do you get the scepter and get back in time?
(From http://www.contestcen.com/contact.htm)
This one also doesn't meet the criteria that the length of the plank must be between 9.48 and 10. I wonder if there is other way.
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rmsgrey
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Re: Crossing water canal
« Reply #7 on: Jan 13th, 2005, 8:48am » |
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This seems like it should work if you can do it (written for the 7m version):
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place 1 plank so that just over 3m of it overhangs the edge directly towards the island. Place a large amount of weight (source unspecified, but at least equal to your weight) on the end of the plank, then use the other plank to bridge the less than 7m distance to the island.
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