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.
Since each point in turn calls the previous brother who spoke a lier, then we have two possibilities. A,C,E are telling the truth or B,D are telling the truth. I chose to assume A,C,E are telling the truth because that seemed to offer alot more information in a positive manner, and if I hit an impossibility, then I would backtrack.
Solution is: Nikolai and Victor are liers, Boris, Vladimar, and Alexis are truther tellers.
On Monday, Karsokovich plays Vladimar, who wins two times. On Tuesday, Ivanovich plays Boris who wins once. On Wednesday, Markovich plays Alexis who wins 4 games, On Thursday, Petrovich plays Victor who wins 3 times, and on Friday Grigorovich plays Nikolai who wins 5 times.
in A, Nikolai plays Friday, and agaist Grigoravich (D) Nikolai did not win 2 more games than Boris, so since Boris won 1 game, he would have to have won 5, since Alexis won 4 and Vladimar won 2.. We know Victor's opponent is not Karsokovich, (B), or Markovich or Ivanovich (C) or Grigoravich (D). So it must be Petrovich. Markovich lost 4 games on Wednesday night (A), and Alexis played him (C). He played two more games than Vladimer (C), and won 4 (A). Boris played against Ivanovich (C), the night before (Tuesday) (C), who only won 1 game (C). I hope I covered all of it. Its getting late.
Posted by dallan
on 2006-03-12 01:53:42