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.

I got the same solution as Diana.

It appears there are 3 scenarios available as far as truth/lying is concerned.

Scenario 1 -
Boris and Alexis True
Victor, Nikolai, and Vlad Lying

Scenario 2 -
Victor and Alexis True
Boris, Nikolai, and Vlad  Lying

Scenario 3-
Nikolai and Vlad True
Boris, Victor, and Alexis Lying

No other combination is possible, and not all of them can be lying.

Scenario 1 works out fine and all the blanks can be filled in.
Monday -  Vic - Petro - 3
Tuesday - Boris - Ivano - 1
Wednesday - Alexis - Marko - 4
Thursday - Vlad - Karso - 2
Friday - Nikolai - Grigo - 5

Scenario 2 works as far as none of the info given contradicts each other, but we still dont have enough information to determine the wins for Mon, Wed, and Fri.

Scenario 3 also works out without contradicting... I think...  but it doesnt lend to nearly the concrete information that scenario 1 does... plus.. Im assuming thee isonly 1 correct answer...  so Im sticking with scenario 1

Posted by Mike on 2006-03-02 23:54:13