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 Brothers Karsakov (Posted on 2006-02-14)
On each of the last five nights, a Karsakov brother played Chess against a different Grand Master. Each brother won a different number of games, from one to five. When questioned on Saturday morning, the brothers gave the following answers.

A. "Nikolai played last night" said Boris. "Grand Master Markovich lost 4 games on Wednesday night."
B. "Rubbish!", screamed Victor. "It was the next night that Markovich lost 3 games. My opponent was Grand Master Karsokovich."
C. "I think you will find," interrupted Alexis, "That it was I who took on Markovich. I can't remember how many games I won but I know it was 2 more than my brother Vladimir. Boris played against Grand Master Ivanovich the night before I played. And Tuesday my Karsokov brother could only win 1 game."
D. "Alexis you are not being honest," said Nikolai. On Thursday night my brother won four games. I won 2 more games than Boris but not against Grand Master Grigorovich."
E. "Alexis," chimed in Vladimir, "Your words are false as always. And it was Grand Master Petrovich who played on Thursday."

Each brother is either a consistent truth teller or a total liar.
On what night did each of the brothers play, who was their Grand Master opponent and how many games did each brother win.

 No Solution Yet Submitted by Vernon Lewis Rating: 3.7143 (7 votes)

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 Solution - spoiler | Comment 7 of 27 |

Since the problem states that each brother is a consistent truth teller or total liar, I take that to mean every relationship given in a false statement is false, and every relationship given in a true statement is true.

Statement A (Boris) and Statement B (Victor) contradict each other. Statement B contends that Statement A is not true. So if A is true, then B is false. If B is true, then A is false. So at this point, I don't know which on is which, but I do know that one statement is false and one statement is true.

Let's skip Statement C (Alexis) for now.

Statement D (Nikolai) contradicts both Statement A and Statement B. Since either Statement A or Statement B is true, then Statement D is false because it is contradicting a true statement. Furthermore, since Statement D says that Statement C is false, and I know that Statement D cannot be true, then Statement C is true.

Statement E (Vladimir) also says that Statement C is false. Since Statement C is true, then Statement E must be false.

Discerning the true statement from A and B was more inferrance than logic.  True Statement C says: "Boris played against Grand Master Ivanovich the night before I played. And Tuesday my Karsokov brother could only win 1 game."

Well, I inferred that Boris and "my Karsokov brother" are two different people. So if Statement A was true, then Alexis would have played on Wednesday, and Boris on Tuesday--that would contradict what I inferred in Statement C. If Statement B was true, then Alexis would have played on Thursday, and Boris would have played on Wednesday. Then, according to Statement C, the Karsokov brother would have played on Tuesday. So, Statement A is false and Statement B is true.

Here are the answers I got:

Nikolai (Liar), Grand Master Grigorovich, 5 games won, Monday
Boris (Liar), Grand Master Ivanovich, 2 games won, Wednesday
Victor (True), Grand Master Karsovich, 4 games won, Friday
Alexis (True), Grand Master Markovich, 3 games won, Thursday
Vladimir (Liar), Grand Master Petrovich, 1 game won, Tuesday

 Posted by Sara on 2006-02-18 23:21:40

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