Repost Puzzle [SOLUTION ADDED]
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Quartz... wrote:
thats the assumption here ( which should be taken as correct )
So if we assume that 1/2 the order can be weighed correctly, just multiply it by 2 to get the weight of the whole order. :rolleyes:
"Approved Workmen Are Not Ashamed" - 2 Timothy 2:15
"Judge not by the eye but by the heart." - Native American Proverb
the assumption is he is able to divide the order in two halfs he cannot weigh any of the halfs accurately Example if he is selling packets of sugar and there are 4 packets he knows that half of them will be two packets , but he won't know that how much woulds be the weight of a single packet or two packets
Omit Needless Words - Strunk, William, Jr.
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Quartz... wrote:
thats the assumption here ( which should be taken as correct )
So if we assume that 1/2 the order can be weighed correctly, just multiply it by 2 to get the weight of the whole order. :rolleyes:
"Approved Workmen Are Not Ashamed" - 2 Timothy 2:15
"Judge not by the eye but by the heart." - Native American Proverb
ding ding. we have a winner.
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Is it a scale or a balance? A balance doesn't have two pans - I don't see how you could put a large dollop of loose lard on the beam side without causing the customer some concern.
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the assumption is he is able to divide the order in two halfs he cannot weigh any of the halfs accurately Example if he is selling packets of sugar and there are 4 packets he knows that half of them will be two packets , but he won't know that how much woulds be the weight of a single packet or two packets
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
It's printed on the packet. And why would he be selling them by weight? Or individually for that matter? And what if the customer is buying a packet of sugar and a watermelon?
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ding ding. we have a winner.
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Since nobody was able to solve it yesterday, i wanted to give a chance to those guys who did not tried Puzzle of the (YESTER)Day A grocer discovered his beam balance was faulty, So he started a new method for weighing customer's orders He divides the order into two halves, putting the first half in the left hand of the balance and weights in the right, then do the opposite. The method is unique no doubt, but is the method fair also, to both his customers and himself ? You can hide , you can run, but you cannot escape, Vote it down if you want to escape i mean if you think the puzzle is not worth a repost. HERE is a sample of PAN Balance[^] SOLUTION[^]
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
Well, if he the scale is off by X, then one side (A) will weigh:
A + X == CounterWeightA
The other (B) will weigh:
B - X == CounterWeightB
So:
CounterWeightA + CounterWeightB = (A + X) + (B - X)
Therefore:
CounterWeightA + CounterWeightB = A + B
Fair, no? But he'll have a heck of a time balancing things if A or B is < X. Of course, he could fix it all by using dead weights to tare the balance first.
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Is it a scale or a balance? A balance doesn't have two pans - I don't see how you could put a large dollop of loose lard on the beam side without causing the customer some concern.
Tim Deveaux wrote:
A balance doesn't have two pans...
Are you sure? Balance: an instrument for determining weight, typically by the equilibrium of a bar with a fulcrum at the center, from each end of which is suspended a scale or pan.
"Approved Workmen Are Not Ashamed" - 2 Timothy 2:15
"Judge not by the eye but by the heart." - Native American Proverb
-
Since nobody was able to solve it yesterday, i wanted to give a chance to those guys who did not tried Puzzle of the (YESTER)Day A grocer discovered his beam balance was faulty, So he started a new method for weighing customer's orders He divides the order into two halves, putting the first half in the left hand of the balance and weights in the right, then do the opposite. The method is unique no doubt, but is the method fair also, to both his customers and himself ? You can hide , you can run, but you cannot escape, Vote it down if you want to escape i mean if you think the puzzle is not worth a repost. HERE is a sample of PAN Balance[^] SOLUTION[^]
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
OK, you've posted an image a balance; now how exactly is the balance faulty? If one of those pan supports were to break, there would be no way to use the balance until it's fixed.
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the assumption is he is able to divide the order in two halfs he cannot weigh any of the halfs accurately Example if he is selling packets of sugar and there are 4 packets he knows that half of them will be two packets , but he won't know that how much woulds be the weight of a single packet or two packets
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
Quartz... wrote:
he cannot weigh any of the halfs accurately
So why is the scale even being used then?
"Approved Workmen Are Not Ashamed" - 2 Timothy 2:15
"Judge not by the eye but by the heart." - Native American Proverb
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the question asked is Whether the method applied by the grocer is fair ?
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
Quartz... wrote:
the question asked is Whether the method applied by the grocer is fair ?
No, since you've previously indicated that "he cannot weigh any of the halfs accurately." That constraint alone nullifies any attempt at weighing the order by 1/2, 1/4, etc.
"Approved Workmen Are Not Ashamed" - 2 Timothy 2:15
"Judge not by the eye but by the heart." - Native American Proverb
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Tim Deveaux wrote:
A balance doesn't have two pans...
Are you sure? Balance: an instrument for determining weight, typically by the equilibrium of a bar with a fulcrum at the center, from each end of which is suspended a scale or pan.
"Approved Workmen Are Not Ashamed" - 2 Timothy 2:15
"Judge not by the eye but by the heart." - Native American Proverb
Ooops - I meant to say a beam balance...
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HERE is a sample of PAN Balance[^]
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
Yes - I meant to say beam balance[^]
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the question asked is Whether the method applied by the grocer is fair ?
Omit Needless Words - Strunk, William, Jr.
Vista? Soapbox Videogadget here
No, you also asked to know the reasoning. Simply saying, "no, it isn't fair" isn't enough.
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Customer orders X quantity of something. Let Y = X/2 Now he measures out Y amount by putting the stuff on the Left and a weight on the Right. Assume there's an error of Z% where the balance is biased towards the Right one. So he actually weighs out (Y - Z% of Y) Now he measures out Y amount by putting the stuff on the Right and a weight on the Left. Since the error works in the customer's favor now, what's weighed out is (Y + Z% of Y) Putting the two quantities together, he gets :- (Y - Z% of Y) + (Y + Z% of Y) = 2Y = X So, the customer gets exactly the amount he wanted. No cheating at all.
Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
Currently working on C++/CLI in Action for Manning Publications. (*Sample chapter available online*) -
Well, if he the scale is off by X, then one side (A) will weigh:
A + X == CounterWeightA
The other (B) will weigh:
B - X == CounterWeightB
So:
CounterWeightA + CounterWeightB = (A + X) + (B - X)
Therefore:
CounterWeightA + CounterWeightB = A + B
Fair, no? But he'll have a heck of a time balancing things if A or B is < X. Of course, he could fix it all by using dead weights to tare the balance first.
Tom Welch wrote:
he could fix it all by using dead weights to tare the balance first.
Yes, so the fact that he didn't leads me to believe that the balance is not as predictable as that. Therefore completely unreliable.
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Well, if he the scale is off by X, then one side (A) will weigh:
A + X == CounterWeightA
The other (B) will weigh:
B - X == CounterWeightB
So:
CounterWeightA + CounterWeightB = (A + X) + (B - X)
Therefore:
CounterWeightA + CounterWeightB = A + B
Fair, no? But he'll have a heck of a time balancing things if A or B is < X. Of course, he could fix it all by using dead weights to tare the balance first.
Does this math still hold if the error is
A*Xinstead ofA+X? Continuing farther does it hold forA+B*(C+X). You really need to quantify how it's erroring, otherwise there're a potentially infinite number of failure modes that would need tested.-- Rules of thumb should not be taken for the whole hand.
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Customer orders X quantity of something. Let Y = X/2 Now he measures out Y amount by putting the stuff on the Left and a weight on the Right. Assume there's an error of Z% where the balance is biased towards the Right one. So he actually weighs out (Y - Z% of Y) Now he measures out Y amount by putting the stuff on the Right and a weight on the Left. Since the error works in the customer's favor now, what's weighed out is (Y + Z% of Y) Putting the two quantities together, he gets :- (Y - Z% of Y) + (Y + Z% of Y) = 2Y = X So, the customer gets exactly the amount he wanted. No cheating at all.
Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
Currently working on C++/CLI in Action for Manning Publications. (*Sample chapter available online*)Nishant Sivakumar wrote:
Let Y = X/2
how is that division accomplished?
image processing toolkits | batch image processing | blogging
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Nishant Sivakumar wrote:
Let Y = X/2
how is that division accomplished?
image processing toolkits | batch image processing | blogging
Chris Losinger wrote:
how is that division accomplished?
Say the customer wants 4 pounds of wheat. Y is now 4 pounds. So X becomes 2 pounds. You take a 2 pound weight and put that on the Right balance and weigh out 2 pounds (with error). Then you swap balances, putting the 2 pound weight on the Left balance. So you basically weigh twice, but 2 pounds each to get 4 pounds. The balance is faulty, but because you do it twice but from opposite balances, the errors cancel out.
Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
Currently working on C++/CLI in Action for Manning Publications. (*Sample chapter available online*) -
working. I didn't see an obvious answer and can't take half an hour to scribble on a scratch pad.
-- Rules of thumb should not be taken for the whole hand.
dan neely wrote:
working. I didn't see an obvious answer and can't take half an hour to scribble on a scratch pad. --
I believe I've answered it correctly - and if my answer is right, it's a pretty simple puzzle.
Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
Currently working on C++/CLI in Action for Manning Publications. (*Sample chapter available online*)
