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Brothers Karsakov (Posted on 2006-02-14) Difficulty: 3 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): Solution - spoiler | Comment 13 of 27 |
(In reply to re(3): Solution - spoiler by Vernon Lewis)

I went about this a little differently. Sara, I agree that statements A and B contradict each other, but only with respect to Markovich. Since Nikolai in statement D is not talking explicitly about Markovich, he is not necessarily contradicting B.

I see definite contradiction between C and D-E. If Alexis is telling the truth, then Nikolai and Vladimir are lying. And vice versa.

Starting with the hypothesis that Alexis was lying, I found Boris to be lying as well. From there, since Vladimir and Nikolai both had to be telling the truth, Victor would have to be lying. I fiddled around a little and came up with this solution, which seems to pass the tests:

Boris, Victor, and Alexis are lying; Nikolai and Vladimir are telling the truth.

On Monday, Alexis won 1 game against Grigorovich.
On Tuesday, Victor won 2 games against Markovich.
On Wednesday, Nikolai won 5 games against Ivanovich.
On Thursday, Vladimir won 4 games against Petrovich.
On Friday, Boris won 3 games against Karsokovich.

Any problems with that solution?


  Posted by Diana Senechal on 2006-02-24 22:43:29
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