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Topic: Old but fun: the cucumber problem (Read 2467 times) |
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WombatDeath
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Old but fun: the cucumber problem
« on: May 21st, 2003, 2:25pm » |
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Right, I've looked through the entire history of easy puzzles on this board and I can't find this one. Once again, apologies if I missed it.
For whatever reason, you buy 400 kilos of cucumbers. These consist (by weight) of 99% water.
After a few days some of the water has evaporated. The cucumbers now consist of 98% water. How much do they now weigh, in total?
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Speaker
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Re: Old but fun: the cucumber problem
« Reply #1 on: May 21st, 2003, 7:12pm » |
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Okay, this is a math problem, but I am willing to put in my two cents worth (2% worth) anyway.
I guess that the first thought is that they now weigh one percent less at 396 kilos.
But, they have only lost 1 percent of the weight of the water which is 99 percent of the total.
So they have lost 1 percent of 99 percent of 400.
Which is.... 396.04. I almost said 392.06 which is maybe the second level trick.
If this is correct, just send the prize money to my favorite charity, the "National Association for Cold Beer". 
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Leo Broukhis
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Re: Old but fun: the cucumber problem
« Reply #2 on: May 21st, 2003, 8:24pm » |
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No, first find out the dry mass, then recompute for the new water percentage. You'll be surprised.
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otter
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Re: Old but fun: the cucumber problem
« Reply #3 on: May 21st, 2003, 8:55pm » |
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The way I figure it, the original weight is composed of 4 pounds kilos solids and 396 pounds kilos water. After a few days, the solids portion still weighs 4 pounds kilos but now the water comprises 98% of the total weight. If x is the total weight of the system (water plus the solids), then x-4 is the weight of the water and (x-4)/x=0.98. Solving for x yields x=200 pounds kilos total.
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| « Last Edit: May 22nd, 2003, 8:27pm by otter » |
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Speaker
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Re: Old but fun: the cucumber problem
« Reply #4 on: May 22nd, 2003, 1:41am » |
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Okay.
I know I'm getting myself into when I try these.
At first I wanted to claim that Otter's answer, while correct, did not respond to the question. But, that would have put me in a bigger hole.
Then, falling back on old methodologies, I tried to figure it out. So, used Otter's formula to calculate the original weight. And, it works, that is plugging in the original weight gives the original distribution of dry and wet mass (weight).
So, Otter must be right. But, how can losing only approximately one percent of the water come out to such a large sum. If we ignored the dry mass, then the loss couldn't be so large could it? What am I missing? 
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redPEPPER
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Re: Old but fun: the cucumber problem
« Reply #5 on: May 22nd, 2003, 3:41am » |
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It didn't lose 1% of the water. It lost more than half of the water. That's how the riddle works: it makes it look that all that was lost is 1%. It isn't. What the riddle really says is that initially there were 99 parts of water for the part of non-water, and that after evaporation there were 98 parts of water for two parts of non-water, or 49 parts of water for the original part of non-water.
99 turned into 49, not into 98 like the riddle tries to make you believe 
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Speaker
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Re: Old but fun: the cucumber problem
« Reply #6 on: May 22nd, 2003, 5:14pm » |
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Okay, I think I am getting it now.
But, just wanted to clarify my earlier post. I said that Otter was correct, but he is not. His is wrong, by a factor of about 2.205. Just wanted to get my pound of flesh.
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They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
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otter
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Re: Old but fun: the cucumber problem
« Reply #7 on: May 22nd, 2003, 8:25pm » |
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on May 22nd, 2003, 5:14pm, Speaker wrote:Okay, I think I am getting it now.
But, just wanted to clarify my earlier post. I said that Otter was correct, but he is not. His is wrong, by a factor of about 2.205. Just wanted to get my pound of flesh.
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I thought I was wrong once, but I was mistaken. I know I should have said 200 kilos, not pounds, but it was late, I was tired, the dog ate my homework and must be because I had the flu for Christmas and I'm not feeling up to par. Actually, my mind took a short trip to the islands. I was so damned happy to get the math right that I didn't check the units. Mea culpa. <g>
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
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T.S. Eliot
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Chronos
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Re: Old but fun: the cucumber problem
« Reply #8 on: May 25th, 2003, 10:49am » |
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Oh, come on, otter, that's no way to weasel! You should have said that you're from Ganymede, where a pound and a kilogram are the same! Well, not exactly Ganymede, but that's closer.
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otter
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Re: Old but fun: the cucumber problem
« Reply #9 on: May 26th, 2003, 2:50pm » |
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on May 25th, 2003, 10:49am, Chronos wrote:| Oh, come on, otter, that's no way to weasel! You should have said that you're from Ganymede, where a pound and a kilogram are the same! Well, not exactly Ganymede, but that's closer. |
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That's my story and I'm sticking to it! 
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
and know the place for the first time.
T.S. Eliot
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