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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 2 of 27 |

Victor/Boris disagree on what night GM Markovich played (Stmts A and B)
Nikolai/Alexis disagree when Nikolai says that Alexis lies (Stmt D)
Nikolai/Boris disagree on what night someone lost 4 games (Stmts A and D)

Pictorially – disagree-ers are next to each other on different lines.

Boris          Alexis

If Nikolai is telling the truth, then Boris and Alexis are lying and thus Victor and Vladimir are telling the truth. However, from Stmts B and D, Victor and Nikolai disagree on the number of wins on Thursday. This makes one of them a liar. If either is lying then Boris must be telling the truth; Victor and Nikolai are both liars; Alexis is telling the truth and Vladimir is lying.

It follows (solving left to the reader):

Alexis (truth)/ GM Markovich / Wednesday / 4 Wins

Boris (truth)/ GM Ivanovich / Tuesday / 1 Win

Nikolai (lies)/ GM Grigovich / Friday / 5 Wins

Victor (lies)/ GM Petrovich / Monday / 2 Wins

Vladimir (lies)/ GM Karsokovich / Thursday / 3 Wins

 Posted by Leming on 2006-02-14 18:27:37

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