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Courk · Daedalian Member

One of my reading assignments contained this quote:

Zag · Tired of his old title

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

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

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!

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

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

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.