# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Author Message
Courk
Daedalian Member

Posted: Fri Jan 11, 2013 4:43 pm    Post subject: 1

One of my reading assignments contained this quote:

 S. S. Stevens (1946) 'On the Theory of Scales of Measurement', SCIENCE, Vol. 103, No. 2684 wrote: Given three balances, for example, each having the proper construction, a set of standard weights could be manufactured without it ever being necessary to place two weights in the same scale pan at the same time. The procedure is too long to describe in these pages, but its feasibility is mentioned here simply to suggest that physical addition, even though it is sometimes possible, is not necessarily the basis of all measurement.

I'm curious, now. What's the method involving three scales?
Zag
Tired of his old title

 Posted: Fri Jan 11, 2013 5:13 pm    Post subject: 2 I am just guessing, but I suspect that you can put one scale (with two pans) in place of a pan on another scale. Assuming that there is a base that never moves, and any of the three scales can be put on it. Any other scale can be used to replace one of the pans on the scale on the base, or it could replace a pan on the scale that is already replacing a pan on the base. Each pan weights one ounce. Scale 1, panless, weighs two ounces, or I could add a single pan (letting it hang lopsided) for three ounces, or both pans for four. Scale 2, panless, weighs 8 ounces. Scale 3, panless, weighs 15 ounces. I believe I can now weigh any integer amount from 1-25 ounces and I don't even have any weights, yet.
Courk*
Guest

 Posted: Fri Jan 11, 2013 8:20 pm    Post subject: 3 He does say balances of proper construction, but that feels like cheating, though it may be the only way. Is there any way to do it without getting to specify the weights of the balances or pans?
L'lanmal
Daedalian Member

 Posted: Sat Jan 12, 2013 1:37 am    Post subject: 4 I'm imagining that the fulcrum is in different locations on the three scales. For instance, one allows you to exactly double (or half) an existing weight. But it is not clear to me why you would need three of these scales rather than just one or two. Perhaps the standard set of weights includes multiples of 2, 5, and something else?
Thok
Oh, foe, the cursed teeth!

 Posted: Sat Jan 12, 2013 1:40 pm    Post subject: 5 I feel like I need more information about what I start with and what I'm making. That said, I assume you can do things like compare how much a scale tilts when you put putative weight A in one scale pan and putative weight B in the other scale pan of a given scale. (I'm imagining an old school scale that a representation of the Lady of Blind Justice would carry.)
Elethiomel
Daedalian Member

 Posted: Sat Jan 12, 2013 5:33 pm    Post subject: 6 If you can adjust the position of the fulcrum, you could e.g. position it a third of the way from one end and two thirds from the other. Then the weight on one side would be twice that on the other, when the scale is balanced. Then again, that's very similar to how traditional scales work, so this doesn't sound like the solution to a puzzle.
groza528
No Place Like Home

 Posted: Sat Jan 12, 2013 5:58 pm    Post subject: 7 I'm not sure I understand the definitions being used in the statement. We're "manufacturing" a set of "standard" weights? Can't we just have one balance that weighs 1kg, "manufacture" the 1kg weight by balancing it against the lightweight balance, then "manufacture" the 2kg weight by balancing against the light balance and the 1kg, etc? Can we "properly construct" our balance with cavities in the pans of specified volumes and then "manufacture" our weights out of ice? What constitutes "standard" weights? 1, 5, 10, 25, and 100kg? because that simplifies the problem. Well, until we have to maneuver the 100kg weight.
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersAnonymousCourkElethiomelgroza528L'lanmalThokZag Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum