Yeah, just relative distances as if the hands moved in straight lines.[tab]10h = 120m
h = 12m
xh = xm/12
10xm - xh = xm
10xm - xm/12 = xm
10xm = 13/12 xm
xm = 12/13 * 10
xm = 9.23076923076923[/tab]
Carleas:
[tab]
That seems like a silly thing to be saying.
You propose one set - the visible.
I propose the possibility of others sets - the partially visible.
You have to “deduce from a set of colors” regardless of which way you go with it.
But the whole set isn’t known by anyone but the master. No one can see the whole set of headbands so none can claim to be certain of all colors, at least until they do some deduction.
No. Until you prove that your proposal has no possible contradicting proposal/algorithm (“lack of alternative”), any of the patterns that I have given are as valid as yours. If you can claim that yours is not an assumption, I can claim that mine aren’t either, “because the problem is solvable”.
No. That is what you are failing to accomplish right now.
We already went through that. Your syllogism assumed that any unseen color is a member of an infinite set and therefore not deducible. That was silly. Every color is always a member of an infinite set. That has no bearing on whether it can be deduced. For an example, one can deduce from the assumption (permitted by the “it is solvable” premise) that the only missing color from the primary & secondary colors is the color being worn.
Again, you say that they can assume that each member can see all puzzle colors and I say that they can assume that the only missing color from a known color chart is a part of the puzzle. We can both make that assumption based upon the master’s premise that it is solvable. And there are other examples wherein an assumption can be made so as to make the puzzle solvable - as long as it can be proven that there is no possible contradicting alternative.
The question is whether there is an assumption that can be made that causes there to be only one way to solve the puzzle. Even if you assume that the seen colors are the only colors, you still have to prove that there can not possibly be any recognizable pattern or formula that could be used, even by God. - THAT is what you have not even begun to prove.
I don’t want to bother getting into longer and longer arguments. This one issue is enough to prevent anything else from being relevant.[/tab]