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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Solution - Spoiler (Quibble) | Comment 4 of 27 |
(In reply to Solution - Spoiler by Leming)

I actually have a little problem with Leming's technique, although I assume his answer is correct (I haven't checked).

The problem is that if two people make inconsistent statements, you cannot conclude that one of them is telling the truth.  They might both be lying!

Specifically, if Boris is lying, it does not necessarily follow that Victor is telling the truth.  At least, it doesn't follow (as Leming asserts) from the fact that Victor says Markovich played on a different night.  It does follow from Victor's "Rubbish!" exclamation, which says that Boris' statement is false.

 Posted by Steve Herman on 2006-02-15 12:06:04

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