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.

(In reply to re: Solution - Spoiler (Quibble) by Steve Herman)

Steve,

I agree with your statement. In fact I had the same issue when I went back and looked for responses to my post.  When I re-read my post I thought: Two lies do not make a truth.

So what can we prove? Nikolai and Vladamir both call Alexis a liar. If these statements are true, then both Nik and Vlad are truth-tellers and Alex is a liar. With Nik disagreeing with Boris and Victor, this would also make them liars.
From this set-up, few facts can be determined and one cannot disprove the statement that Nikolai is telling the truth.

Adding an assumption:  From Stmt B "Rubbish", Victor is calling Boris a liar.

This would lead to the conclusion that either Victor or Boris is telling the truth. Then, whichever one of these two were telling the truth, their disagreement with Nikolai would make Nik a liar.
If Nik is a liar then so is Vlad, and Alex is telling the truth.

So its left to decide who between Victor and Boris is lying.  Assume Victor is telling the truth and Boris is a liar. I found the following:
Alexis (Truth) / GM Markovich / Thursday / 3 Wins
Boris (Liar) / GM Ivanovich / Wednesday / Unknown
Nikolai (Liar) / GM Grigorovich / Monday / Unknown
Victor (Truth) / GM Karsokovich/ Friday / Unknown
Vladimir (Liar) / GM Petrovich / Tuesday / 1 Win

This does not disprove the assumption that Victor is telling the truth.

And as was seen in my previous post, you can also assume that Boris is telling the truth and be unable to disprove it.

So, no single solution works.

Posted by Leming on 2006-02-16 13:36:15