No, no you didn't understand 100% what i've said!

You say that i have to prove that a solution is correct.
And why i have to follow the direct way you have in your mind obviously?
I want to follow, as i did, the indirect way.
That is:

-Take as valid what the author said about the problem and call it statement A.
A = "there is a mate in 2 for white in this position".
I can do it and trust him when he said: "there is a mate in 2 for white in this position" BECAUSE the author defines his problem that way. That is:
Gave us a position and said that A is true. THIS IS THE PROBLEM.
And a problem owns to be right of course(I guess here is where you disagree.More on this later).

-Take as a statement B to be: B = "black can castle"

-Prove that B => A'
-And since A' is false we have immediately that B must be also false so:
-B' is true. So:
-Black can't castle! (1)

-And then since (1) is true, we just show that 1.Qa1 (any black move) 2.Qh8 mates!

I can't explain it more clearly!


You objection should come from the fact that I USE the statement "there is a mate in 2 for white in this position" of the author as true.
But i can do it, because it's the part of the problem!
If the author didn't want to be the part of the problem then he should not have said that.
He should say find the shortest mate in this position for white. Then my second solution would be the correct one.
But now that he made a valid statement the "there is a mate in 2 for white in this position", we can use it for our favor to solve the problem!

I hope you understood me now.....


Oh, so you propose that we should not trust the author of a problem that he gave a valid problem! Now i understand your above thoughts.
Yes, if we accept that a puzzle may be wrong(in this case for example that the author's tip of "there is a mate in 2 for white in this position" can be wrong) then my first solution is not correct.
Only my second as you said.

But when i read a problem or a puzzle of that form, i ALWAYS take as granted that is a valid one.
It would be ridiculous if someone said: "Here is a position, white to play and mate in 4, can you find the mate? I assure you that there is a mate!" and a mate in 4 would not occur.
It would be totally ridiculous if the problem was not correct.
Since we are not supposed to show the validness of the authors statement but only to solve what the author tells us to solve with his statement.



Yes here is we disagree. The disagreement is easy to spot and resolve since i accept the author's statements about the problem as valid, while you don't accept them as valid or invalid. It's not that i'm correct and you are not or the opposite. You just want to solve not the problem the author gave but a general problem. I want to solve the problem the author gave.

For example: Person A, gives us to prove that: "Cats have 4 red feet. We take a cat and remove one of her feet. How many red feet the cat would have now?"

I solve it like this: TAKE as true all the statements of the problem/statement person A gave. I do that because i want to solve the problem he gave not anything else. So:
-The cat we took had 4 red feet. I take that as true.
-We removed one red foot. I take that as true.
-So the cat now has: 4-1 = 3 red feet!

You solve it like this: Not accept as true the statements of the problem/statement the person A gave. You do this because you don't trust what the author says want to solve the problem as also to prove the validness of the problem. So:
-The cat we took had 4 red feet. You don't accept that as true or not true.
-So you can't show the validness of the author's statements of the problem.
-So you can't solve the problem.


And that's the problem with this philosophy of not accepting as true what the author of the problem has said: You can't solve most of the problems.


And let's go to the problem we had here:
The author of the problem, gave:
1)A Chess position which is just a statement of the form: "We have a Chess position with a FEN: ././././././."
2)A statement of the form: "White can mate in 2 from this position"
3)Give the mate in 2 for white.

The first 2 are statements the author gave.
The last is the question.

-You propose that we shouldn't accept the statement 2).
-OK, but why we should accept the statement 1) ?
-If we don't accept what author said so clearly, about the mate in 2 the white player has, then WHY to accept the validness of the position the author gave?
-If we accept that the author can give wrong things, then why should we accept that the position he gave is correct?
Well simply we can't accept it!


In this problem we can either accept ALL the statements the author gave, as i did and solve the problem, or we should not accept his statements and try to prove them.
In the second case which is what you are saying is the correct thing to do, we have to prove: the validness of the statement 1), that is to prove the position the author gave is wrong, and also the validness of the statement 2), that is to prove there is a mate in 2 for white.
And while it is easy to prove there is a mate in 2 for white, it is impossible to prove that the position the author gave is correct.
So we CAN'T prove that the statements 1) and 2) the author gave are correct.
Also we can't be selective as you were, about which of the statements the author gave are correct. Why to choose that the position he gave is correct and that "white has a mate in 2" can be wrong?

We should try to solve the problem he gave and not to prove that the problem he gave is true or not.


No! My "theory" DOES NOT say this!
My "theory" says that(and without saying again all the details):

Since white has a mate in 1:
It is true that:
1.cxd6 OR 1.gxf6 is a mate in 1.
So:
1.cxd6 OR 1.gxf6 is a solution.

And if we exclude one of the moves(by retrograde analysis for example) then we would find the single solution.