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 I thnk this is it... too by Highway6)

Scenario 1 - Boris and Alex - Truth
                - Vic, Nik, and Vlad - Lie

Scenario 2 - Vic and Alex - True
                - Boris, Nik, and Vlad - Lie

Scenario 3 - Nik and Vlad - True
                 - Boris, Vic, Alex - Lie

How I got the 3 scenarios....

Niko and Vlad both say Alex is lying. They both make the same statement... therefore
If N=true then Vl=true
If Vl=true then N=true
If N=false then Vl=false
If Vl=false then N=false
 Niko and Vlad can not be opposites.

Going down the list one at a time assuming each brother is telling the truth.....

Assume B=true then Vi=false, N=false, Vd=false, A=True
 Vi conflict - wins associated with Marko
 Nik conflict - day associated with 4 wins

Assume Vi=true then B=false, N=false, Vl=false, A=true
  Boris conflict - wins associated with Marko
  Nik conflict - wins associated with Thursday
 
Assume A=true then N=false, Vl=false
  Nik and Vlad  - both say Alex is lying.. which cant be true under this assumption

Assume N=true then Vl=true, A=false, B=false, Vi=false
  Alex conflict - cuz Nik says so
  Boris conflict - day associated with 4 wins
  Vi conflict - wins associated with Thursday

Assume Vl=true then N=true, Alex=false Vi=false, B=false
  Has to match above assuming N=true
 
 
 
 
 
 

Edited on March 6, 2006, 12:54 pm

Posted by Mike on 2006-03-03 00:33:44