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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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 re: Solution - Spoiler | Comment 6 of 27 |
(In reply to Solution - Spoiler by Leming)

I agree with the rest of the comments that Nikolai and Vladimir are liars, Alexis is truthful and we can not assume about Boris and Alexis.

Just a remark on this post. If we accept that Boris is thruthful then Vladimir won 2 games and Victor won 3. This is because as Alexis stated he won 2 games more than Vladimir.

Now, for the problem about which one, Boris or Victor, lies, I suggest that the wording of the puzzle should be changed as followed "Their questioner knew who was truthful or not and he understood in which night each brother played, with whom Grand Master and how many games they won".

 Posted by Magda on 2006-02-18 20:37:50

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