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===The puzzle===
The puzzle is to find the flaw in the line of reasoning in the switching argument. This includes determining exactly ''why'' and under ''what conditions'' that step is not correct, to be sure not to make this mistake in a situation where the misstep may not be so obvious. In short, the problem is to solve the paradox. The puzzle is ''not'' solved by finding another way to calculate the probabilities that does not lead to a contradiction.
'''I.'''
'''I.Еfimov's explanation''':
''The first explanation:'' "In fact, the paradox is apparent, there is only a ridiculous mistake in the formulation of the problem. For some reason, it is assumed that there are three values, a certain X, 2X and 0.5X. This immediately indicates an incorrect wording. In fact, there are only 2 options, either 2 times less or 2 times more. There is no middle X. Thus, we need to formulate the problem as follows: let's take for X a number that is less than 2 times. There are 2 options: I have X, the second has 2X, or I have 2X, the second has X. You will either win X as a result of the exchange, or you will lose X. There is no paradox."
''The second explanation:'' "There are 2 parties involved in the exchange. So why are we only considering one side? The second person thinks the same way. He has X, I have either 2X or 0.5. It is assumed that the initial conditions are equal for both sides. Thus, the initial states are not 2, but four:
a) The first has X, the second has X/2
b) The first has X, the second 2X
c) The second has X, the first 2X
d) The second has X, the first X/2
==Multiplicity of proposed solutions==
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