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.

This solution is based on Vernon Lewis's previous clarification of the ambiguity in line C of the game:

"Since posting I have realised of the ambiguity possibilities. I meant statement C to be interpreted as: Alexis was speaking of two different days; and refers to two different brothers.
Seperate sentences refer to different situations.
I should have written - Tuesday another Karsokov brother could only win 1 game." (Lewis)

With Lewis's clarification in mind, assuming:

Boris & Alexis = truth tellers / Victor, Vladamir & Nikolai = liars

...then I believe the answer would be:

Monday / Boris (5-0) / Ivanovich
Tuesday / Victor (1-4) / Petrovich
Wednesday / Alexis (4-1) / Markovich
Thursday / Vladamir (2-3) / Karsokovich
Friday / Nikolai (3-2) / Grigorovich

I believe this is correct.

Posted by jeff on 2006-05-30 09:51:46