Fabio Capello has accepted the post of coach of Kazakhstan. Two hours ago he has landed in the country, and without even knowing the players, he must lead the match against Sweden in World Cup qualifying for 2014 Brazil.
To choose the lineup, Capello decides to repeat the one of the last match played. The problem comes when the right-back, Shomko gets injured.
Capello knows that Gorman and Kirov are defenders, but he's not sure if any of them play down the right. In addition, Capello has been told that, in this national team, all players who play down the left are jokers and always lie, while those playing on the right flank always tell the truth.
Fabio comes up to the two players and ask them if they play on the right wing.
|Gorman - Kirov|
Gorman replies that Kirov and he play by the left flank.
If right-backs tell always the truth, and left-backs always lie, would Capello be able to use one of these two players as right-back, or should he keep looking on the bench for another player to occupy the position?
If Gorman played on the right flank, he would always tell the truth, and therefore he would have said that he's a right-back (at this time we don't care about what he says about Kirov).
However, Gorman said he plays by the left flank. This means that he's not a right-back who tells always the truth, but a left-back that always lies. So we already have a player eliminated for replacing the injured one.
Now let's go for Kirov. The problem we have is that he hasn't said anything. So we have to find out his position based on what his playmate has said.
We know that Gorman is a left-back. Suppose that Kirov is also a left-back. Then, when Gorman said that he and Kirov played down the left, he would have told the truth.
But we know that Gorman is lying. Therefore, Kirov can't be also a left-back, but he necessarily has to be a right-back, such that the phrase 'Kirov and I are left-backs' be false.
So now we know which player Fabio Capello will choose to replace the injured player: the right-back Kirov.
This enigma is in honour of Lewis Carroll, the excellent british writer, famous worldwide for his work Alice in Wonderland. He brilliantly developed another subjects, like photography and recreational mathematics, and wrote quite interesting riddles and paradoxes such as the paradox of the caterpillar and the lizard, which is the base of our present problem.
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