h a l f b a k e r yWarm and Fussy
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Next time someone gives you 12 gold coins and warns you "...but one of them is counterfeit and has a different weight from the others, and you don't know whether the different one is heavier or lighter than the real ones, and you are only allowed to use a balance scale two times..."
AMAZE them with
your triple balance three-way weight-comparing "Counterfeit Buster" apparatus! This three-trayed triangular gadget will always fall in the direction of the tray that is the heaviest, and should two trays tie for heaviest, the pair will lower together, causing the lighter tray to rise.
Now you can solve what's been an age-old headache with ease, by simply placing 4, 4, and 4 on the three trays; then choosing the mismatching group of four and weighing 1, 1, and 1, leaving one out. The result of the second weighing identifies the culprit lickety-split.
Force Table Ilustration
http://www.physicsc.../vectors/U3L3a.html
How is this different from a force board (or table)? [spiraliii, Oct 10 2005]
[link]
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At last, a solution to this most vexing problem. I will sleep well tonight. |
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I'm sure there are other applications for this. I'm slightly concerned that unlike [Texticle] I will not sleep until I have thought of at least one. |
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Speeds up dividing bricks of cocaine, among other things. |
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But all three bricks will have slightly different weights. Or you have encountered more precise drug dealers than I ever have. |
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//How is this different from a force board (or table)// |
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It's different because it's a lot nicer looking, packaged with red circular trays, a manual giving step-by-step instructions on how to deduce the fake item from a set of up to 2048 items in the minimum number of uses, and three arrow-pendulum readouts, one on each side of the scale. |
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Oh, and the warranty is much longer than that of a traditional balance scale, since this one requires fewer uses per task. |
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It seems like an N-balance scale would be more convenient. Just set
N=12 and put a coin in each tray. |
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There's much to be said for a pair of trays and the patience to set differences aside. |
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N = 12 would not work. Because if two coins opposite each other tied for heaviest, the scale wouldn't show you that. |
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It has to be 3 sides or fewer. But a two-sided scale is just too inefficient, and here at the 1/2 bakery we do not tolerate inefficiency. |
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