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| Thread: The bucket problem (creative thinking) | |
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Miru
Supreme Hero
A leaf in the river of time
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posted June 06, 2007 06:00 AM |
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The bucket problem (creative thinking)
There is a famous problem, often used in IQ tests or riddles, to test spacial reasoning. The problem goes, you have a 5 Unit (gallons or litres or whatever) bucket and a 3 U bucket. They are unlabeled. You are also given a hose which pours water. You are asked to measure out exactly 4 U.
When asked about the problem a trained psychologist will tell you there are two answers. However, there may be more.
If you haven't solved this problem and would like to don't read on as I will give the two obvious ways away next.
1) Fill the five, fill the three from the five, leaving two left in the five. Pour the two in the five into the three. Fill the five. Fill the three from the five (taking one out), leaving four.
2) Fill the three. Dump the three into the five. Fill the three. Fill the five from the three, leaving one. Dump out the five. Pour the one left in the three into the five. Fill the three. Pour that into the five.
But what if you want to save time, and water?
There are many alternate methods.
My dad thought of:
Tilt the two buckets and raise the meniscus to be half the bucket:
Leaving 1 1/2 U in the three, and 2 1/2 U in the 5. Pour the three into the five
NOTE: this only works if the bucket are symmetric.
My brother (RTI) thought of:
Fill the five. Displace three of it by pushing it out with the three:
Many things can be done to get to four from there.
NOTE: this only works if the buckets are not very thick, and the 5 is strictly bigger than the three (if they have the same diameter then you can't put the three in the five)
I thought of:
Count how long it takes you to fill the five. Divide that time by 5, multiply by 4, and pour for that long into the bucket.
No picture 
NOTE: this is only practicle with a hose (not if you're filling from a well of a lake), and only possible if the water is steady pouring (constant rate) and you are good at counting.
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Also you can do it ways irrelevant to the buckets, like sell the two buckets and buy a four.
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What ways can you think of to do it?
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I wish I were employed by a stupendous paragraph, with capitalized English words and expressions.
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alcibiades
Honorable
Undefeatable Hero
of Gold Dragons
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posted June 06, 2007 12:38 PM |
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Quote:
My dad thought of:
Tilt the two buckets and raise the meniscus to be half the bucket:
Leaving 1 1/2 U in the three, and 2 1/2 U in the 5. Pour the three into the five
NOTE: this only works if the bucket are symmetric.
This is quite clever. I would like to add, though, that the constraint that the buckets have to be "symmetric" isn't entirely precise - the buckets have to be cylindrical (having the same radius at top and bottom), otherwise the amount of water remaining in the bucket will be less than half the total volume of the bucket.
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What will happen now?
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