Riddles

[tab]

Next step:

A: “No” => b < 18.
B: “No” => a > 9.

And so on.[/tab]

The whole solution (with the solution process):

[tab]In the beginning A knows that (1) a = 12 or a = 15, and (2) B knows that b = 12 or b = 15.

Okay. But A does not know that B (2) knows, and B does not know that A (1) knows. So the statement above is not suited for the recursive conclusion.

But both A and B know all of the following statements and that each of them knows that the other one knows them:

(3) a = 24 - b or a = 27 - b and (4) b = 24 - a or b = 27 - a.

Now, from the first “No” of A and from (4) follows (5) b < 24, because if b >= 24, then A would be able to conclude a. This is the motor for the recursive conclusion.

Now, from the first “No” of B and from (3) and (5) follows (6) a > 3.

And so on.

A: “No” => b < 21.
B: “No” => a > 6.
A: “No” => b < 18.
B: “No” => a > 9.
A: “No” => b < 15.
B: “Yes”. Because together with the information of (2) there remains only one possibility.

Now add the „No“s!


The game ends after 7 „no“s.[/tab]

I remind you of the riddle I posted on 14 January 2016:

Who is depicted here?

Easy_Riddle.jpg

Incorrect (for several reasons).
Sorry, try again. :sunglasses:

My solution is absolutely correct.

Your “there-is-no-solution-solution” is incorrect.

That is incorrect. Sorry. Try again. :sunglasses:

“Famous last words.” :sunglasses:

You should know me well enough to at least accept a tiny bit of doubt if I am telling you that you are incorrect.
Would I say it without a reason? :sunglasses:

My actual words were:

First correction:
You must disqualify zero and all negative numbers when you word the riddle, else your count will be different.

Agreed?

No.

The said riddle:

So I wrote in the said riddle: “this numbers are positive integers (thus also no zero)”.

It seems that you have not read the said riddle.

Oops … your right, I missed that (silly me). My apologies. One must VERIFY anything I say (age n all). :blush:
… so on to the next issue:

Second correction:
This is the issue with all such “perfect logician”, “recursive” riddles.

Being so perfect, they both already know that the other knows this sort of game. Even without being perfect, both you and I know of this algorithmic method. And the whole issue is to be able to realize what the other person knows so that each member can depend upon the answers being given by the others.

As with the “Blued eyed puzzle” and all such similar algorithms, there must be a number with which to begin. You chose “24”, as most people would. But perfect logicians are not “most people”. They know to choose, from the many options, the starting point that would lead to the least number of rounds. The question is “how many no’s are required?” They could have begun their count at 48 or at 100. That would be silly. Why would they? But then again, why would they start at 24?

In all of these scenarios, the place a more perfect logician would begin is the number that is the closest that both parties would necessarily not be able to resolve the puzzle by knowing. They both want for the first “no” to be informative, telling them of something they didn’t already know. They both see a “12” and thus both know that the other knows that the only options for any party is either:
[list]9
12
15[/list:u]

It is a waist to begin at 100 and count your way down when you already know that nothing is going to be resolved until you get close to those numbers. It is also silly to begin with 24 for the same reason. Both parties know that they could begin at any number higher than 15, but can’t choose which number unless they privately begin the known algorithm at 24 (the lowest known sum) and simply count to themselves down to “18” (or merely add the difference of the sums to the 15). They both can deduce from the beginning that neither would be able to say “yes” if they began from the number 18. Thus that is where to begin.

a) They both already know that both already know that their number is <18.

b) And that means that after the first “no”, they both know that their number is >9, eliminating one of the possibles.

c) Second “no”, their number must be <15, eliminating a second possible, leaving only one possible number.

Puzzle resolved with more perfect logicians with only 2 "no"s.

But that isn’t my last objection/“correction”.

Advantage for me. 1 : 0 (one to nothing). :slight_smile:

It is your first correction, because your “first correction” was no correction but a mistake of you that was corrected by me. So it was my first correction. Therefore: Advantage for me. 1 : 0 (one to nothing). :slight_smile:

Okay. Now I can only say what you have said:

The said riddle I posted about three month ago was a copy (the first copied riddle I posted). I did not question that there were too many "no"s in the text, because I did not question the whole copy, and that was my mistake. I am sorry. My apologies. The next riddle will be one of my own thoughts again, I can promise. You are right: One must VERIFY anything. But sometimes one is too busy or too lazy to do it anytime.

Advantage for you. 1 : 1 (one to one). :wink:

No. But it was your first correction. =D>

Counting feathers are we. :laughing:

Now see, if you were Carleas, you would argue this issue with me for the next 20 PAGES (as he did with the Blue eyed puzzle, another similar riddle, and the Stopped Clock Paradox). Some men just can’t stand to lose a feather (those with too few). [-(

Now let me “Re-Riddle” something from this riddle:

Re-Riddle:
Two men, John and Gerry, are walking along with a clearly visible number written on their foreheads.
John asks Gerry if he knows what number is on his own forehead.
Gerry honestly answers “No”.
Gerry then asks the same of John.
John also honestly answers “No”.
Then Gerry says, “Oh okay, my number must be X.”
Immediately John replies, “Oh, then so is mine.”

Now the question:
What must they have known about their numbers before John asked Gerry if he knew his own number?

… and doesn’t it seem eerie that such could actually happen. :open_mouth:

Gah, James, you got it smartpants.

I was close though.

If a solution is possible, then they have to know a certain number range, thus the upper limit and the lower limit of the range of their numbers, and they have to know another aspect, for example: a possible sum, a possible difference, a possible product, a. possible quotient of their two numbers (for instance: Gerry only knows a sum of the two numbers of a certain number range, whereas John only knows a product of the two numbers of the same certain number range).

If a solution is not possible, then they have to know how to order two beers. :laughing:

Bier_und_Alt-Bier.jpg

In any case, ordering two beers could actually happen. Couldn’t it? :laughing:

A little vague.

I didn’t know Mithus was a beer drinker. :-s
:obscene-drinkingcheers: [size=85]{{hmmm… how come his is bigger than mine}}[/size]

Three perfect logicians walk into a bar.
The bartender says "do you guys know what you’re having?
The first one says: “No”
The second one says: “No”
The third one says: “Yes”

:laughing:

No.

John and Gerry, who are walking along with a clearly visible number written on their foreheads, have to know a certain number range, thus the upper limit and the lower limit of the range of their numbers, and they have to know another aspect, for example: a possible sum, a possible difference, a possible product, a. possible quotient of their two numbers (for instance: Gerry only knows a sum of the two numbers of a certain number range, whereas John only knows a product of the two numbers of the same certain number range). So they know enough, even more than enough (!), in order to solve the riddle.

The primises in the riddle “Perfect Logicians” are enough too. Again:

A and B know enough in order to solve the riddle.

If it is said that two humans see a number, then we can surely assume that this humans are capable of seeing and reading, and of knowing what they see and read. That is common sense.

[tab]Who is depicted here?

The following solution is false:

[/tab]

Solution:
[tab]1) A, C, D
2) B, E, F[/tab]

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

Looks an awful lot like:
[tab]



[/tab]

That is right. =D>

What about the solution process? :wink:

:laughing:

That is false.

Try again.