Arminius wrote:So I wrote in

the said riddle: "

this numbers are positive integers (thus also no zero)"

Oops .. your right, I missed that (silly me). My apologies. One must

VERIFY anything I say (age n all).

... 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:

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".