Math Fun

That is false.

Please read the text one more time.

Well done, James. =D>

What about the solution process?

Hey, my job is to answer questions. Your job is to figure out how I got the answers.

[size=85]… just be sure to always disagree at least once so that I have incentive to go check my work …
[/size]

lol… the product, not the sum!
Facepalm…

Let me guess twice:

1. By reading, understanding, thinking, and calculating.
2. By finding the answers in the internet.

If I could look up the answer, I could look up the process for obtaining it.
I don’t go to that trouble for mere games.

1. I’ve presented a logical syllogism, using mathematical induction, which is a method of deductive mathematical logic.
2. As we’ve already discussed, once you have a syllogism, you don’t need to show that there are no other syllogisms (see e.g. the Pythagorean Theorem)
3. Even if it were the case that I needed to show there were no other solutions, for the MI problem I’ve provided a syllogism that shows that N islanders cannot learn their eye color before day N, so if there were another syllogism, it would produce the same result.

It is true for certain premises. If we assume X and ~X, we can conclude Y and ~Y. I’m saying that “this problem is not impossible” is an exotic premise that could similarly produce contradictory conclusions. I don’t think it does, but much of your argument seems to depend on it.

Right, but you’ll notice that I only said that the syllogism is “clearly valid”. The point being that a valid syllogism can be constructed using “this problem is not impossible” as a premise, and challenging you to show that the syllogism shouldn’t be treated like any other.

Do you agree that “colors don’t bear any logical relation to each other” is a true premise? Or do you have a similarly true premise that leads to a contradictory conclusion?

Only AFTER you skipped over substantiating your most essential premise (your presumption of colors) as well as your presumption that a faster method of color discovery could not be used.

Carl, that is stupid. Why do you keep saying that? Do you not read criticisms of your propositions? That is just a dumb thing to say and I have explained why. Once AGAIN:
[size=150]We are NOT talking about many proofs for the same outcome.[/size]

We are talking about the need to prove that there cannot be any other possible [size=150]outcome[/size], and thus no other possible algorithm/solution.

No, you have NOT. I showed you that everyone could easily leave after the second bell. You are simply not listening.

No, it isn’t.

It would be true if you made sense of it first, but as stated and knowing the context, I have to deny it. Colors have a natural relative ORDER (most often expressed as a frequency). An order isn’t technically “a logical relation”, but it is an association that can be used in a logic argument: “Green is between yellow and blue. Purple is between red and blue. Orange is between red and yellow.”
One of the premises is that “it is solvable”, so…

And also the presented colors CAN have a displayed order:

Procrastinating…

dice game
[tab]A=10 (2 and 5)
B=15 (3 and 5)
C=9 (3 and 3)
D=20 (4 and 5)
E=12 (2 and 6)

Solution process: I put it on a spreadsheet

[/tab]

Well done, Phoneutria. =D>

Did you post your method for that, and I missed it, Arminius? I’d like to see it, because I pretty much brute forced it.

[tab]In your excel sheet you can place true/false statements for the critical concerns along with the calculated numbers. Then merely count from 1 to 36 and one cell will tell you when you have the right number (“10”) by saying “TRUE”. All of the other numbers will be already calculated.

What they are calling “quantum computing” works that way except they assign a different CPU to each number between 1 and 36 so that all possibilities are computed in parallel. The first CPU that registers a “TRUE” stops the process. In that way, the time it takes to calculate the answer is always as if you already knew the “10” to try first.

If this were 20 years ago, I would spend some time trying to come up with a way to combine logic and math so as to directly cause the “10” answer to pop out from a single, albeit very long, equation. But these days, my brain is too tired.[/tab]

I guess you mean the solution process.

[tab]1st round = x.
2nd round = x + 5.
3rd round = x + 5 - 6 = x - 1.
4th round = x - 1 + 11 = x + 10.
5th round = x + 10 - 8 = x + 2.

All possible throw combinations:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36.

A possible combination in each round is only possible with x = 10:

1st round = 10.
2nd round = 15.
3rd round = 9.
4th round = 20.
5th rounde = 12.[/tab]
So as I already said: Well done.

Armie,

[tab]So your solution, as well as mine and James involve iterating from all possible values until one matches. That’s what I wanted to know, if that is the way to go about it, or if there is a way to derive a formula that would arrive at 10 without trying all the possible results.
Thanks.[/tab]

James,
[tab]You have already acknowledge that your examples are not alternatives:

So, there may be some scientific induction that can be done given your set ups, but there is no deduction that could lead the logicians to conclude their headband color.

Again, I submit that “colors don’t bear any logical relation to each other”. There is no syllogism of the type, “red, yellow yellow, blue blue blue |- green”

Moreover, 1) with regard to your first example, every other logicians would realize that the logician with the orange headband would have no logical way to conclude her headband color, and 2) with regard to your second example, we’ve already discussed how there are an infinite number of completions to any pattern.

To the rest, I’ve specified two parts to the problem: the Set Restriction (SR) part, and the Mathematical Induction (MI) part. The parts are distinct. The MI part takes as one of its premises what is proven in the SR part, but the logic of the MI part is just the logic of common knowledge that solves the Blue Eyes problem and its variations. The SR part is still under discussion, I haven’t skipped it, I’m just giving you the MI syllogism and asking you to respond to it at the same time. It is, after all, a part of the solution on offer (not to mention that it is a widely accepted solution to the Blue Eye problem which you obstinately refuse to accept, and I think you should).[/tab]

Carleas,[tab]

I told you that my examples were a reflection of your example, each merely making a convenient assumption that allows the puzzle to seem like it is solvable, even though in the final analysis, it actually isn’t.

Carl, you are just doing as I said that you were going to do back at the beginning of this; repeat yourself over and over while ignoring my counter arguments (although you did manage to muster up the answer to one usually ignored question). You seem to be incapable of seeing the obvious but perhaps are merely wrapped up into an ego concern of one type or another. In either case, you appear to not really care of the truth of this matter and thus I no longer care to discuss it with you. Your “Blue-eyes” class of puzzles are not being validly addressed.

But Wiki is in error in many articles, so this one wouldn’t be anything exceptional.[/tab]

[tab]

And I distinguished my proposed solution from your examples: my proposed solution relies on deductive logic of the form “if X → impossible, ~impossible |- ~X”. Your examples do no such thing, they are (and you’ve acknowledge they are) scientifically inductive, and thus not based on deductive logic.

Your attempts at psychoanalysis aside, I’ve responded to every argument you’ve made clearly and directly. Indeed, when your arguments were good, I’ve acknowledged as much and revised my arguments to address your valid points; you have ever reason to believe that a valid criticism clearly expressed will be seriously considered and result in a revision of my position, as it has on multiple occasions).

And while of course Wikipedia can be wrong about common knowledge, the syllogism I’ve offered (which you haven’t bothered to address directly, i.e. by pointing to a specific line that you have a problem with) is not original to Wikipedia. When you doubt wiki’s accuracy, follow the sources: look at the Stanford Encyclopedia of Philosophy and its entry on the problem. A Nobel Prize winner built his most famous work on it, read his paper.

There are two possibilities: You have actually identified a defeater of the logic at play, and refuse to reveal it clearly even though it would clearly be a significant achievement; or you have not, and you care not to discuss it because you care not to admit it.

If you would admit it, we could focus on the SR, where I think you have a real possibility of being right (although I still think you’re wrong about that too).[/tab]

Repeating yourself and ignoring me by copying and pasting an allegation that I’m repeating myself and ignoring you? Very meta.

Time to end the discussion, I think.