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        riddles >> easy >> Old but fun: the cucumber problem
        
(Message started by: WombatDeath on May 21^st, 2003, 2:25pm)

Title: Old but fun: the cucumber problem
Post by WombatDeath on May 21^st, 2003, 2:25pm

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?

Title: Re: Old but fun: the cucumber problem
Post by Speaker on May 21^st, 2003, 7:12pm

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....[hide] 396.04[/hide]. I almost said [hide] 392.06[/hide] 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". :-/

Title: Re: Old but fun: the cucumber problem
Post by Leonid Broukhis on May 21^st, 2003, 8:24pm

No, first find out the dry mass, then recompute for the new water percentage. You'll be surprised.

Title: Re: Old but fun: the cucumber problem
Post by otter on May 21^st, 2003, 8:55pm

The way I figure it, [hide] 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. [/hide]

Title: Re: Old but fun: the cucumber problem
Post by Speaker on May 22^nd, 2003, 1:41am

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? ???

Title: Re: Old but fun: the cucumber problem
Post by redPEPPER on May 22^nd, 2003, 3:41am

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 :)

Title: Re: Old but fun: the cucumber problem
Post by Speaker on May 22^nd, 2003, 5:14pm

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.

Title: Re: Old but fun: the cucumber problem
Post by otter on May 22^nd, 2003, 8:25pm

on 05/22/03 at 17:14:55, Speaker wrote:

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>

Title: Re: Old but fun: the cucumber problem
Post by Chronos on May 25^th, 2003, 10:49am

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.

Title: Re: Old but fun: the cucumber problem
Post by otter on May 26^th, 2003, 2:50pm

on 05/25/03 at 10:49:11, 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.

That's my story and I'm sticking to it! 8)