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.

All right, so I think we've established that Alexis is telling the truth, and both Nikolai and Vladimir are lying. So then, either Boris or Victor must be telling the truth, but not both.

If we assume that Victor is telling the truth, then we run into an indefinite situation. We can figure out who played whom on which days, but some of the numbers are uncertain. However, if Boris is telling the truth, then we have a definite solution:

We know that Nikolai played on Friday (A) and that Alexis won 4 games against Markovich on Wednesday (A, C). We know that Boris played on Ivanovich on Tuesday and won 1 game (C). We also know that Nikolai played Grigorovich (D). So far, this is what we have:

Tuesday: Boris played Ivanovich and won 1 game
Wednesday: Alexis played Markovich and won 4 games
Friday: Nikolai played Grigorovich.

Now, to fill in the blanks, we have all the information we need. Victor lies when he says he played Karsokovich (B), so he must have played Petrovich. Vladimir lies when he says Petrovich played on Thursday, so Petrovich must have played on Monday. Now we have this:

Monday: Victor played Petrovich.
Tuesday:  Boris played Ivanovich and won 1 game
Wednesday: Alexis played Markovich and won 4 games
Friday: Nikolai played Grigorovich

So, who is left? Vladimir and Karsokovich, who must have played on the one remaining day, Thursday. In addition, we know that Alexis won 2 more games than Vladimir (C). Therefore:

Monday: Victor played Petrovich.
Tuesday:  Boris played Ivanovich and won 1 game
Wednesday: Alexis played Markovich and won 4 games
Thursday: Vladimir played Karsokovich and won 2 games
Friday: Nikolai played Grigorovich

Now, Nikolai is lying when he says he won 2 more games than Boris (C). Therefore he could not have won 3 games. Therefore, he must have won 5 games, and Victor 3:

Monday: Victor played Petrovich and won 3 games
Tuesday:  Boris played Ivanovich and won 1 game
Wednesday: Alexis played Markovich and won 4 games
Thursday: Vladimir played Karsokovich and won 2 games
Friday: Nikolai played Grigorovich and won 5 games

It seems that this solution works. The only thing that's bugging me is that the other option (where Victor is telling the truth) should lead to a contradiction or impossibility. I only see it leading to several possible answers. So I suspect I'm misinterpreting or missing something...

Posted by Diana on 2006-02-25 10:50:31