Math Fun

You used 100 twice and you should only use it once. Which one you use (/100 or 100*) depends on if the answer is in euros or cents.

James, please read what I wrote in my last post again:

[tab]What has been holding us both up is more the fact that you did not take my advice. For example this:

That must be a whole number.

[/tab]

This objection is overcome by the stipulations about how good a logician the participants are. To turn again the 2 Blue Eye problem as the simplest case of the logic, if there are 2 blues on the island, it seems clear that two perfect logicians, for whom it is common knowledge that they are perfect logicians, will know their eye color on the second day. There is no reliance on a everyone being “in sync” or using the same “theory”, there’s is pure deductive logic about what the islanders know and how they must behave and how they must deduce from their knowledge and behavior.

Returning to the case of the Master Logician, I take the same level of logical perfection to be a given, as the Master will enforce accurate deduction on the other logicians. It’s not whim or fancy that he’s enforcing, but what the logicians must deduce based on what they know and how they must behave and how they must deduce from their knowledge and behavior (or have such deduction forced on them by the master). The effect is the same.

Is that what you’re taking issue with here? I admit the premise is implicit; a more-clear statement of the problem would be explicit in the way the Blue Eyes problem is.

No… “e” is merely a number of objects received and so is “c”, although different objects.

The statement was that those two numbers got reversed: the e number was supposed to be the c number and vsvrsa.

But when translating those numbers into money values, the e number was supposed to be the number of cents, thus

e/100 = amount of cents (proper)

And also the c number was supposed to be the number of euros, thus

c*100 = amount of euros (proper)

So “e/100 + c*100” should be the amount of proper returned change (“entitlement”).

But if that was true, it would mean that the received NUMBER of objects, “e + c” had to be 2.55102040816327, which is obviously not possible.

Thus there is a miscommunication going on, as I said in the beginning.

The stipulation that the logicians were perfect demanded that they were in sync as a premise. This puzzle doesn’t have that stipulation. But even if it did, the puzzle would be unsolvable (or at least by you).

Well, that was not a given, but like I said, even if it was…

You didn’t solve the Blued problem either, so referring it doesn’t get you anywhere.

The fundamental problem is that you must PROVE that no other possible means for solving the problem can exist. And I have already provided you with several ways equal to yours (you merely deny that yours is just as good). One of those ways directly defeats your assumption by allowing you to make that assumption while also proving a means for everyone to leave by the second bell.

Again, again, and again, you merely keep saying the same thing over and over, that you think your assumed premise is the only possible valid assumption. You haven’t proven that. And repeating it over and over does not prove anything other than inference that there actually isn’t the actual proof that you need.

Please don’t say no when you don’t know.

If you have amount represented as e.c …
then the amount in cent is equal to 100e+c
and the amount in euros is equal to e+c/100

For example :
10.27
e=10, c=27
10.27 (in cents) = 1027 = 100*10 + 27
10.27 (in euros) = 10.27 = 10 + 27/100

I DO know. I am the one who defined it.

That I know too. But that is not what I had asked Arminius.
To which he answered:
“if the proper entitlement is x, e is the received euros, and c is the received cents, then 2x + 5 = e + c” and
“if the received euros and received cents were confused, then the proper entitlement is, x = e/100 + c*100”

That seems like a big proviso. Unsolvable-in-theory is a relatively tiny subset of unsolvable-by-me-in-practice :smiley:

Happy to keep that conversation going, if you would deign to respond to my syllogisms. Note, off the bat, that they are pure deductive syllogisms relying on the islander’s common knowledge and required behavior, and not on any islander being “in sync” with any other. Like with the Pythagorean theorem, the deduction itself is the proof that no other solution is possible.

Nope. You merely jump ahead ignoring that your presumption is merely one possibility that allows you to then rush into deductive reasoning. You do that on both problems, “rush to satisfying judgement”. It is a very common mental ailment of the day, especially of attorneys who intentionally try to bias themselves toward their client (prosecution or defendant).

There is no “judge” on this site to call you down to order. So you just keep repeating yourself and being non-responsive. I have explained your errors at every turn. You simply don’t care … not a big issue on a site like this.

Yeah, and of mathematicians and Nobel prize-winning economists and authors of encyclopedias on philosophy, who apparently also foolishly believe that deducing a proposition X is the same thing as deducing a proposition ~(~X). How wacky!

I do care, James. Deeply. I care because failures of reason irk me. Society works best when people are rational, and rationality works best when people are honest with themselves.

And, be honest, you’ve never pointed to a specific part of the deductive proof of the solution to the Blue Eye problem. You’ve never grappled with the mathematical induction being used. You’ve avoided treating in an intellectually honest way, preferring to mock and hand-wave and declare the discussion over and insinuate a failure of reasoning on the part of anyone who disagrees with you. But none of that changes the validity of the solution. None of that even addresses the solution. The solution to the Blue Eye problem can be shown in many ways, has been shown in many ways, has been analyzed by people much more accomplished in math and logic than you or I and has stood the test of honest and rigorous attempts at defeat. If you think you can defeat it, do so honestly, do so rigorously, do so academically. It would honestly be an accomplishment.

He gave you a bum steer. All his equations are wrong.

Complete strawman.

I don’t believe that one for an instant. You never go to the trouble of looking down that other logic road/option. People who care that they are really right, not merely appearing to be right, go to that trouble. You obstinately avoid it. Either you are hard-hypnotized into being hard-blind to specific concerns, or you simply care more about something else enough to not bother checking out the other option.

Well, at least you know the words … a shame that you don’t care.

Be honest. I pointed to specific reasons why your deduction is irrelevant, not fallacious.
Blued puzzled:
“If everyone is thinking this …”
But what IF they weren’t?

Master Logician Puzzle:
“If we assume that only the colors we see apply, then…”
But what if something else is assumed?

You consistently jump to an easy assumption and go from there, never looking back to verify that your assumption is provable. You just get to an answer and then, apparently in glee, ignore that your starting point was presumptuous. In a courtroom with a jury, that tactic probably would allow an attorney to get away with a great many injustices, as is normal throughout the USA at least. But in a court of logicians, that tactic simply doesn’t fly. Logicians don’t easily forget that your premise assertion was never proven to be necessarily true.

Logicians are not merely jurors.

Bullshit. I had more math in college than you … and then proceeded into engineering, using it.

This is just more of your rhetoric. Great for attorneys in a court of law, not a court of justice.

===============================================================================

Yeah, that is all that I was trying to say. :sunglasses:

Then why do you keep using those equations??? :open_mouth:

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. :sunglasses:

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. #-o

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).