Silly question. I had to use them in order to ask if that is what he meant. He is saying something that others are not hearing to mean what he really means to say.
If the change due was 34.56, the cashier gave back 56.34 instead. That’s it in a nutshell. 
You’ll note that none of my syllogisms contain either of these antecedents:
Blue Eye Syllogism 1
Blue Eye Syllogism 2
Master Logician Syllogism 2
I think we all agree with that.
[tab]If e = 34, the received euros, and
c = 56, the received cents then
the proper change (“entitlement”) was said to be
x = c.e => 56.34 => 100c + e, in cents (5634 cents)
x = (100c + e) / 100, in euros
x = c + e/100, in euros
Premise: 2 times the proper change was received plus 5 cents more:
2x + 5, in cents was received.
The received euros is “e” and the received cents is “c”, so:
2x + 5 = e + c, wherein each e = 100 cents and each c = 1 cent
So:
2x + 5 = 100e + c, in cents, or
2x + .05 = e + c/100, in euros
and
x = 100c + e, in cents
x = c + e/100, in euros
thus using merely cents,
2(100c + e) + 5 = 100e + c, in cents
100c + e + 2.5 = 50e + c/2
100c - c/2 = 50e - e - 2.5
c(100 -1/2) = e(50-1) - 2.5
99.5c = 49e - 2.5
c = 49e/99.5 - 2.5/99.5, in cents (thus e must be at least 6)
And then another equation is required to finish it and find x.[/tab]
…edited my booboo.
Yes. Your syllogisms do not because you SKIP OVER the assumptions that you are making. That is why your syllogisms are irrelevant.
You are misstating YOUR presumption as a given premise. Your presumptions are wrong thus your following syllogisms are meaningless.
I gave the correct equation and you turned it around. 
This is the answer:
[tab]Let P be the price of book in cents
Let A be the amount of change due from 100 euros in cents
A= 10000 - P
Let R be the returned change in cents
R= 2A + 5
The amount of change due can be represented as E.C
Therefore A and R can be written as:
A= 100E + C
and
R= 100C + E
Substitute these into the previous equation (R=2A+5) and you get :
100C + E = 2(100E + C) + 5
which rearranges to give :
C= (199E + 5)/98
The only value of E which results in an integer value for C is 31
E=31 and C=63
Calculate A and P :
A=3163
P=6837
Price of book was 68.37 in euros.[/tab]
Actually you turned it around in your answer (marked in red). I had defined the e and c in terms of received, not owed (and underlined it several times).
You turned it around by multiplying by 100 in one equation and dividing by 100 in the other. If you define it in terms of cents then both equations would have multiplications by 100.
It was only a matter of defining “e” as what was received versus what was owed.
I defined it as what was received.
You ignored that and redefined as what was due.
That is the only difference (other than me leaving out a later division operation).
You just can’t admit that you make mistakes. :-"
I just did, DS. But my mistakes do not translate into the lack of yours. You screwed up and now can’t admit it.
I have made mistakes in the past and I will make mistakes in the future.
James, please! Note: Phyllo is right. You have to admit that you made mistakes in the said case.
Okay wake up!
I mentioned the exact mistakes that I made. He denied the ones that he made (possibly still unaware).
Neither of us are claiming to be perfect.
Get your shit straight if you are going to get into the middle.
NOTE!: Phyllo made a mistake in his original complaint because he didn’t realize the definition of “e” that was being discussed. He intruded, unaware of the details. End of that story. He later provided the answer … fine. I have no disagreement with his answer. I provided just short of that answer (trying to not give it all away). In doing that, I made one division error that I pointed out and corrected.
This is NOT an issue of either one of us being egotistical. It is an issue of phyllo not seeing that he had overstepped into an already established discussion (thus redefining the terms). After that point, there was no right and wrong, merely two rights that were different in their nature (due to differently defined terms; specifically “e” and “c”). And then you stepping in, completely blind and making an … of yourself.
Yes. It is okay.
I shall be magnanimous and let James have the pleasure of demonstrating the last part of the solution - calculating E or C from his final equation. 
Just put your answers in reverse, into the equation that I provided. You will get the same result. I merely had e and c defined (before you intruded) to be the opposite of what you chose … no big deal. It works either way.
Cool. =D>
By the way, I’m not sure how you defined DS. Does it stand for dipstick, dip shit, dumb shit or something else? I would like to know in case you use it again in the future. 
Yeah, I know…
… Dear Saint. :-"
First, it’s important to note that this premise is not that same as “If everyone is thinking this …” It’s not logically equivalent, and the former does not implicitly assume the latter.
Second, this is a given. We know this because 1) they must deduce anything deducible, and 2) they have been on the island for an infinite number of days prior to the Guru speaking. If there were a way for them to deduce their eye color prior to the Guru speaking, they would have. The problem goes to length to rule out other means of learning their eye color: there are no mirrors, they can’t otherwise communicate, they don’t already know it. In infinite time before the Guru speaks, nothing has let them learn their eye color, and nothing else happens on the island that could communicate their eye color to them.
Similarly to the above, this is not logically equivalent to “If we assume that only the colors we see apply, then…”
But to address the objection, I think it must be a failure of communication. Each color of headband that any logician can see is the correct answer for at least one logician in the circle to the question “what color is my headband?” That’s tautologically true. Each color of headband that any logician can see is worn by at least one logician: the logician that is wearing it. Sorry if I was unclear in expressing this premise, but properly stated, it cannot be false.