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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 w/ Reasoning | Comment 22 of 27 |

I agree but here is my reasoning as well.

Day        Brother   Wins      Opponent
Monday       Victor        3            Petro

Tues           Boris          1            Ivanovich

Wed           Alexis          4            Markovich

Friday          Nikolai        5           Grigorovich

I came to this by Boris and Alexis telling the truth and Victor, Nikolai and Vladimir always lying.  By this, I was given the Tuesday Wednesday lines and Nikolai playing Friday night.

I then assumed that the liars said everything opposite.
For Victor:   It was not Mark on Thurs who lost 3, but the brother who played on won 2.  If Alex was true than Vlad won 2 games, thereforehe played on Thurs.  Victor can also not play Kar.

For Nik: Thurs the brother did not win 4, we already know it was Wednesday.  It also can't be Nik that has 2 more wins than Boris and the only other person besides Nik we don't know is Victor.  He also says he didn't play Grig which means he did so we have Friday Nik won 5 games against Grig (from deduction)

Vlad: All we know is that Petro didn't play Thurs. and from deduction Victor can't play Kar so he has to play Victor on Monday and that leaves Vlad with 2 wins against Kar on Thurs.

 Posted by Trish on 2006-03-06 00:05:58

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