Monthly Archives: October 2010

More Chessboard

Posted on October 27, 2010 by Vadim Kulikov

You are free to comment your solutions, questions and remarks.. You have two kinds of allowed moves. One move is to jump with a piece over another piece in a horizontal or vertical direction like this: and to jump with … Continue reading →

Posted in Combinatorics, Games, Mathematics, Recreation, Wednesday Problem | Tagged | 3 Comments

Prisoners’ Problem 5

Posted on October 24, 2010 by Vadim Kulikov

There is a famous class of problems concerning public announcements. There is a philosophical (sociological) appeal in these problems. Can a public announcement change the behaviour of the citizens? Of course, if it is for example a news article about … Continue reading →

Posted in Combinatorics, Mathematics, Philosophy, Recreation | Tagged | Leave a comment

Incomplete Chess Board

Posted on October 20, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. I learned this puzzle from Juha Oikkonen, but it is probably quite famous anyway. You have left your chess board on the table in the summer house and when you came back you … Continue reading →

Posted in Combinatorics, Games, Mathematics, Recreation, Wednesday Problem | Tagged | 2 Comments

Map Colouring Problem And Compactness

Posted on October 16, 2010 by Vadim Kulikov

Suppose G is a planar graph embedded into the plane. The graph divides the plane into regions. Let us say that two regions are adjoint if they have a common edge. Question: (Q) Is it possible to colour the regions … Continue reading →

Posted in Combinatorics, Geometry, Logic, Mathematics, Topology | Leave a comment

Poisoned Bunnies

Posted on October 13, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. Imagine that you have one thousand bottles in front of you. You know that one of them is filled with poison and others with water, but you do not know which one is … Continue reading →

Posted in Combinatorics, Mathematics, Recreation, Wednesday Problem | 7 Comments

Using Abstract Algebra To Understand Basic Combinatorics

Posted on October 11, 2010 by Vadim Kulikov

Pascal’s triangle has many fascinating properties. One of them is for any given prime number p, the number of k-element subsets (0< k < p) of a p-element set is divisible by p: [tex]p | \binom{p}{k}\qquad \qquad \qquad (*)[/tex] You … Continue reading →

Posted in Algebra, Combinatorics, Mathematics | Tagged | 5 Comments