Well there should be a solution, it’s just GdB is seemingly switching the situation from unknown to known to try to make his solution work, which is against the rules.
Perhaps he could rescue the situation by saying we can treat the puzzle as if the amounts are known because….............
Something along those lines could convince me but it’s hard to imagine what that something might be.
I don’t have to ‘rescue’ the situation. I already gave my solution (yes, the one with the X’s): the answer is correct, and I say to you, the derivation is too. You asked about a hundred postings ago how I can know that my solution is correct, independent of it ‘accidentally’ giving the correct answer, where kkwan’s solution seems to be correct, but gives the wrong answer. This is answered already many times, not just by me: the unknowns used in kkwan’s formula do not have the same value, and therefore cannot be used as constants in his formula.
The point I am driving at in my recent childish questions, is to give you the feeling that when there are two amounts in the envelopes, that might be unknown by ‘the player’, but the amount that are in the envelopes are in it. They are closed, and what is in one envelope or the other does not change if I pick one envelope first, or then the other.
So IF, by example, there are $10 and $20 in the envelopes, independent of the knowledge of the player about it, there will never be $5 or $40 in one of them. We do not have to think about it.
The player knows that, even if he does not know the amounts, there are only 2 amounts in the envelopes, and therefore can be exhaustively described by X and 2X. If you keep hesitating about this, imagine two values that fit TEP, and see that there are only two amounts. (Come on, do it, take two envelopes and play the game with your spouse/son/daughter/friend!) So the only 2 possibilities are that you pick the smallest amount first, or the largest, i.e. X or 2X. Just think about it: there are two amounts, the smaller and the bigger. But kkwan states there is a third amount that I should reckon with. Does that make sense to you?
To show that, I gave another, TEP-like, situation that fits to kkwan’s derivation. (Read it a few postings back.) The question ‘what is the expected value?’ can be calculated exactly with kkwan’s formula. But it is not TEP anymore. As kkwan is not able to show why his formula does not apply to my TEP-like situation, and by saying this is not TEP, he confirms my point: his formula is not valid in real-TEP.
My only point here is that I am explaining this to you both. You are the only ones in the school class that do not see the point. Your colleagues are home already for a long time, but the teacher tries to give the correct insight to the two last pupils who resist to what is already clear for all the others. One pupil thinks that everything must be more complicated than the teacher says (he has trouble to understand the solution, that it can be that simple), the other one will never give in, because he put all his personal credibility in his wrong derivation.
Listen, I have some mathematical background, and you haven’t both. There was another mathematician on this thread who better than I explained and derived the correct solution, and you both did not recognise it, be it by lack of insight, or by just wanting to be awkward, by trolling.
PS This topic was already in the wrong forum from the beginning. As it is a mathematical problem, and mathematics is a science, it would belong in ‘Science and technology’.