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#1
February 12th, 2003, 03:22 PM
 Scorpions4ever
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Weighing Puzzle - Another Brain Exercise

All right folks, time for another puzzle to exercise your minds and test your ingenuity. You have a set of scales. You want to measure any weight from 1 to 40 kg.

1. What is the minimum # of weights you need, in order to do this?
2. What are the values of these weights?

I'll post the correct answer in a few days, if no one gets it by then

#2
February 12th, 2003, 03:32 PM
 tony825
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Hint

I know the answer but im not going to write it, for now!

Ill let the others to find it,

Comment : the weights must be of integer values.

Hint : the same can be used IF You want to measure any weight from 1 to 81 kg.
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#3
February 12th, 2003, 03:34 PM
 Scorpions4ever
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Good point tony, I forgot to mention that the weights must all be integer values (though this is more of a hint rather than a restriction)

#4
February 12th, 2003, 04:16 PM
 M.Hirsch
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Q:
Could the problem be described also similar to "which base do you need for a numbering system that you could identify any value between 0 and 40 (39? - what about weighting a zero-weight? you did say "1-40") uniquely and how many digits would you need for an ideal solution?" (sorry for the bad english, hope you still understand my point...)

like for identifying 32 unique values, you can use a numbering system based on 2 with 5 digits (damn, i canī find the words...)
2log32-1=5 -> you would need 5 wages with values of 1 or 0. (Could one still optimize this? probably to a base of 4 or 8, eh?)

I can't make up any other equations for this. School is too long ago

Or am i on the totally wrong track?
Get me a hint please. I am really interested in the solution but i donīt want to break my brain on a "way to nowhere"...
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#5
February 12th, 2003, 04:42 PM
 Scorpions4ever
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Well, you are sort of on the right track there. However you can do it with fewer weights than you're thinking

#6
February 12th, 2003, 04:52 PM
 M.Hirsch
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do you need to be able to weight a zero-weight then or not?

#7
February 12th, 2003, 06:19 PM
 Scorpions4ever
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Nope, you don't weigh a 0 weight. You only need to weigh anything between 1 and 40 kg. (whole numbers only. you're not required to weigh something say 22.5 kg).

To clarify matters, click here to see what a balance scale looks like. Hopefully, this makes the problem clearer.

#8
February 13th, 2003, 06:39 AM
 mathew
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I got it

it could be done with 4 weights.
values are: 1, 3, 9 and 27.

btw. it took's me 15 minutes to solve this.

#9
February 13th, 2003, 09:19 AM
 Strike
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Warning - discussion of the answer

Unless you can place weights on both sides of the balance, then the 4-weight solution above won't work. It can't measure something weighing 2kg. If you can't place weights on both sides of the balance, then you simply do base 2 to get the minimum number of weights to get the answer. I.e., 1, 2, 4, 8, 16, 32 - will weigh anything from 1 to 63 (which doesn't match the hint, so I've got a feeling it's not the correct solution) - using only one pan. But you know it's the minimum number because there's no duplication of combinations that produce the same weight, and taking away any of them would remove several possible weights.
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#10
February 13th, 2003, 12:37 PM
 Scorpions4ever
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Mathew wins the virtual cigar. I didn't put any restrictions on using both sides of the balance . The answer is 4 weights -- 1kg, 3kg, 9kg and 27 kg. To elaborate on mathew's answer further --

For 1 kg - Put 1 kg on one pan
For 2 kg - Put 3 kg on one pan, 1 kg on the other pan
For 3 kg - Put 3 kg on one pan
For 4 kg - Put 3 kg and 1 kg on one pan
For 5 kg - Put 9kg on one pan, 3 and 1 kg on the other pan
...
For 40 kg - Put 1, 3, 9, 27 kg on one pan

Cheers!

#11
February 24th, 2003, 05:35 AM
 Mincer
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Re: Weighing Puzzle - Another Brain Exercise

Quote:
 Originally posted by Scorpions4ever You have a set of scales.

If I had a balance however....

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#12
March 8th, 2003, 05:16 PM
 Jason Doucette
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Quote:
 Originally posted by Strike ...If you can't place weights on both sides of the balance, then you simply do base 2 to get the minimum number of weights to get the answer. I.e., 1, 2, 4, 8, 16, 32 - will weigh anything from 1 to 63 (which doesn't match the hint, so I've got a feeling it's not the correct solution) - using only one pan. But you know it's the minimum number because there's no duplication of combinations that produce the same weight, and taking away any of them would remove several possible weights.
In fact (assuming again that you cannot use both sides of the scale), you can remove weight 1kg, since you only need to weigh 1, 2, 3 .. 40kg (integer amounts). Without the 1kg weight, you can determine any weight that is a multiple of 2. Since there exists only one possible weight that cannot be weighed exactly between each possible weighing of an exact number, then you can determine these weights. For example, if you have a mass of 5kg, then you can determine that it weights more than 4kg, and less than 6 kg. There is only one possibility: 5kg.

Last edited by Jason Doucette : March 8th, 2003 at 05:18 PM.

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