The potato paradox
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Richard MacCutchan wrote:
So if you lose 1% of the water, isn't that just 1lb less than before?
lets work through this. if this were the case. 100lb total, 1lb startch, 99lb water water = 99/100 = 99% of total - 1lb water = 1lb startch, 98lb water, total 99lb water = 98/99 = 98.9898989... % it is not 98.0% yet.
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I was quoting @Richard-MacCutchan and was trying to help explain (to myself aswell) that losing only 1lb water would NOT give 98.0% but only works out to 98.98...% and that the correct number is something else.
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I was quoting @Richard-MacCutchan and was trying to help explain (to myself aswell) that losing only 1lb water would NOT give 98.0% but only works out to 98.98...% and that the correct number is something else.
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You have 100 lb of "mathematical" potatoes, which are 99 percent water by weight. You let them dehydrate until they're 98 percent water. How much do they weigh now? No googling, ok.
Wrong is evil and must be defeated. - Jeff Ello
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You have 100 lb of "mathematical" potatoes, which are 99 percent water by weight. You let them dehydrate until they're 98 percent water. How much do they weigh now? No googling, ok.
Wrong is evil and must be defeated. - Jeff Ello
WEIGHT_OF_POTATOES = 100 lbs
WEIGHT_OF_WATER / WEIGHT_OF_POTATOES = 0.99
WEIGHT_OF_WATER = WEIGHT_OF_POTATOES * 0.99WEIGHT_OF_WATER = 99 lbs;
(WEIGHT_OF_WATER - weight_to_evaporate) / (WEIGHT_OF_POTATOES - weight_to_evaporate) = 0.98
(99 - weight_to_evaporate) / (100 - weight_to_evaporate) = 0.98
weight_to_evaporate = 50 lbs;So the final answer is WEIGHT_OF_POTATOES - weight_to_evaporate = 100lbs - 50lbs = 50lbs
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You have 100 lb of "mathematical" potatoes, which are 99 percent water by weight. You let them dehydrate until they're 98 percent water. How much do they weigh now? No googling, ok.
Wrong is evil and must be defeated. - Jeff Ello
Trust the math. Given 100lb = 99lb-water + 1lb-potato w = weight of water in lbs % water = w / (w + 1lb-potato) Initial condition = 99%. Check. Now solve for 98% water .98 = w / (w + 1lb-potato) w = 49 lb Check: 49 / (49 + 1) -> .98 add back the 1 lb of potato and the total is 50 lb total
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Sorry, I have the (usually good) habit of at least quickly glancing through all the replies before I add a comment. So I saw the answer before starting to consider the problem myself. But the problem is a good one! (Although not a true paradox.) Semi off track (but only semi!): It reminds me of a Norwegian sausage maker boasting his sausages having a 133% meat content. Advertising authorities protested: No product, not even a boneless steak, can contain more than 100% meat. This slaughter insisted that he used 1,33 kg meat to make 1 kg of these cured (smoked and dried) sausages. This went to court, where it was pointed out: When the meat is weighed, it contains a lot of water that weighs as meat. In the production process, when the sausages are dried, some of this water is removed. If that water was labeled as meat when you weighed the ingredients before you started, it is actually part of the meat that is removed during the drying. You can't claim that all of the meat is a part of the product when you have removed some of it. So the slaughter lost the case, and had to change the wording from "contains 133% meat" to "For each kg of sausage, 1,33 kg of meat is used". Which isn't too bad - the sausages are tasty! :-)
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Quote:
You let them dehydrate until they're 98 percent water.
That's pretty clear!
Sent from my Amstrad PC 1640 Bad command or file name. Bad, bad command! Sit! Stay! Staaaay... AntiTwitter: @DalekDave is now a follower!
Quote: "let them dehydrate until" The trick is hidden right there. Our brain expects the word to be "rehydrate", so we think it's rehydrating the original 1% dehydrated solids. Caught out by being too quick ...
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Forgive me for being thick but I cannot get my head round that. In 100lb there is 1lb of starch and 99 lbs of water (yes?). So if you lose 1% of the water, isn't that just 1lb less than before?
A: 100lb total, 1lb startch, 99lb water water = 99/100 = 99% of total B: MATH YOUR BRAIN WANTS TO DO BECAUSE OF 100lb: 100lb total, 2lb startch, 98lb water water = 98/100 = 98% of total so far the math makes sense, now the thing is; you did not gain a pound of starch. The startch stays the same so the final answer is: 50lb total, 1lb starch, 49lb water water = 98/100 = 98% of total Norm
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You have 100 lb of "mathematical" potatoes, which are 99 percent water by weight. You let them dehydrate until they're 98 percent water. How much do they weigh now? No googling, ok.
Wrong is evil and must be defeated. - Jeff Ello
100 lb of potatoes have 99% water and so 1% other stuff i.e. 1 lb. After dehydrating, water is lost but other stuff is still in same quantity i.e. 1 lb. Since water is now 98%, the remaining 2% of the total weight is 1 lb. Hence, 1 lb is 2 % of the total weight. So, the total weight is 50 lb.
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Nothing is clear in the land of language....
