I’m pretty sure this isn’t what you mean, but it’s true:
[tab]1, because that’s the smallest (positive) integer.
Perhaps the question is better posed like this: ]
Suppose the smallest square is 1x1. How big is the largest square?
Is that the same problem?[/tab]
Be careful, because the following tab contains parts of the solution process:
[tab]Choosing the most qualified integer is alraedy part of the task. At first you have to derive equations from the diagram, then you must pay attention to some subtleties, then you have to solve the equations, and after that you should choose the most qualified integer … and so on.
For reasons of simplification you should choose “1” as the most qualified integer for one variable.[/tab]
For ease of reference:
No solution yet, but…
[tab]I did a bit of work on this before I realized that they are all different sizes, which means the whole shape is not a square (otherwise B = C).
So I have to start over, which I will do later. My basic plan of attack is to list out the equations (e.g. A + B = C + E + F, etc.), then let J = 1 and solve for each other variable, then multiply them all by whatever gets them all to be integers (I was wrong earlier, J can’t be 1, because A - (B + H) < J, so if J = 1, either A, B, or H could not be a integer).[/tab]
Just do it.
That is you - always just denying the other route and refusing to even discuss it while trying to press your own point again and again.
If you want to start a thread about the logic of the Blue Eye problem, I’m happy to engage. Instead, you started a thread about a “common mistake” in science and philosophy. And, rather than actually show that these mistakes are present in the canonical solution to the Blue Eye problem, rather than actually laying out your case, rather than quoting what I or anyone who’s endorsed the canonical solution has actually said (instead of making up a quote that is trivially fallacious), you just state that it “dawned” on you and then explore an intro-level logical fallacy.
Whatever prompted you to have your dawning, that thread is not about the logic of the Blue Eye problem. So far, this is the only thread in which that problem has been directly addressed.
This problem is pretty tedious, I think I must be doing it wrong.
[tab]Here are some equations:
A = C+G
B = H+D
B = I+F
C = G+E
D = H+J
E = G+I
F = J+D
H = I+J
A+B = C+E+F
A+C = B+H+I+F
A+G = B+H+I
Should be enough. Let’s try and solve for a variable in terms of J.
A+C = B+H+I+F
(C+G)+C = (I+F)+H+I+F
2(G+E)+G=2(I+F)+(I+J)
2(G+(G+I))+G = 3I+2F+J
5G+2I = 3I+2F+J
F = J+D
F = 2J+H
F = 3J+I
5G+2I = 3I+2(3J+I)+J
5G+2I = 5I+7J
5G = 3I+7J
A+G = B+H+I
G = (H+D)+H+I-(C+G)
2G = 2H+(H+J)+I-(G+E)
3G = 3H+J+I-(G+I)
4G = 3H+J
4G = 3(I+J)+J
4G = 3I+4J
G = (3I+4J)/4
5((3I+4J)/4) = 3I+7J
(15/4)I+5J = 3I+7J
(15/4)I-3I = 2J
(3/4)I = 2J
If J = 1 → I = 1.5
→ H = 2.5
D = 3.5
B = 6
F = 4.5
A+C = 14.5
A+G = 10
C-G=4.5
E = 4.5
G = 3
C= 7.5
A = 7…
Shit.[/tab]
Yep, definitely did it wrong 
Why don’t you properly show your full and clear understanding of the problem that I am pointing out (on the right thread). And then you can clarify the distinction between it and your reasoning. Why do you always avoid doing that every time? We have already annoyed this thread to death with our differences about the Blued problem.
You and I so often seem to take the exact same approach. The difference seems to be that when I find that it isn’t exactly true, I look at different means of tackling the problem. That relates to why your answers to the Blued problem and the Master’s logician meeting puzzle are not valid … you ignore the possibility of alternative methods while the puzzles forbid any.
No more appropriate thread exists. There are many, many threads discussing many, many fallacies that I’m not invoking in my solution to the Blue Eyes problem. I’m not going to go into any of them and explain how that particular logical fallacy doesn’t apply to my solution to the Blue Eyes problem.
And as with your approach to the Blue Eyes problem, you’ve yet to show your work.
Your continued evasion merely proves my point.
OK, found the a problem:
[tab]A = C+G
B = H+D
B = I+F
C = G+E
D = H+J
E = G+I
F = J+D
H = I+J
A+B = C+E+F
A+C = B+H+I+F
A+C = B+H+J+F and/or
A+C = B+H+I+E
A+G = B+H+I
I’ll have to power through solving for something in terms of J later.[/tab]
Carleas???
[tab]
[/tab]
Interesting, a little mind bending, and certainly difficult to express. Here is an attempt:
[tab]The circles are rotating at different speeds, and slower than the wheel. If there we more tick marks on the two circles and on the lines they are ‘riding’, it would be clear that the surface of the circle is moving slower than the string as they pass. That ‘slippage’ accounts for the difference in apparent circumference (the length of the string) and actual circumference.[/tab]
Yep. =D>
Now try to explain where the energy is coming from in this:
[youtube]http://www.youtube.com/watch?v=m8-Kek8Halc[/youtube]
And this:
[youtube]http://www.youtube.com/watch?v=_HV9YWmGf8g[/youtube]
First one
[tab]I think here the magnet acts as a fuel source, a source of stored energy and it will gradually lose effectiveness as the polarity of its atoms moves out alignment over time.
After writing that, I looked it up, and it is wrong… 
OK, second guess: the potential energy from moving the ball away from the magnet is released as the ball moves towards the magnet.[/tab]
Second one
[tab]Here, I’m pretty sure the initial twist of the spring is what’s driving the spinning, and that that energy will gradually be lost as heat.[/tab]
I think that you missed on both counts:
[tab]1) The ball doesn’t move toward the magnet.
2) Note that for every turn of one end of the spring, the opposite end gets exactly one turn. The amount of twist in the spring must remain constant.[/tab]
[tab]In both, there is a subtle periodicity, i.e. they aren’t in smooth motion, but are slightly jerky. In the spring example, that means that the torsion moves through the system like a wave, so that one part twists a bit, then the next, then the next, so that the twist is actually travelling around the system in a loop. It seems the wooden handles act something like a diode, making it so that the twist can only ‘flow’ in one direction.
In the magnet/ball example, the ball rocks back and forth, drawn toward the magnet, and then moves backwards by the spinning wheel. The motion is started when the magnet is pulled away from the ball, so that the magnetic force decreases slightly and the ball falls, starting the wheel spinning. The ball then rolls, which spins the wheel. The wheel itself speeds up and slows down; as it spins faster, the ball is moved farther from the magnet and the magnetic force on the ball decreases, slowing the wheel and increasing the force.
So the ball is moving towards the magnet – and then away, and then towards, and then away…[/tab]
[tab]Ooo! I’ve been had! Treachery!! Fool me a half dozen times, shame on me 
Nice tricks though, clever setup. The one with the spring seems to have a motor in the frame, it looks like hits a switch with his right hand just as it starts spinning. I can’t figure out the other one, but I’m thinking it has something to do with the silver block used to hold the magnet.
The magnet car was a bridge too far, I knew that one was no good.
Thanks for making me providing me the opportunity to look like an asshat, James. =D>[/tab]
[tab]Nonono… you are selling yourself short. These are from VEProjects. They don’t use tricks. They merely don’t tell you everything so that you can figure it out. There are no hidden motors involved[/tab]