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- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
- The Product of Topological Spaces Does Not Obey Cancellation October 12, 2011
- Wild Embeddings October 11, 2011
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- Douglas Hofstadter: I Am a Strange Loop. August 15, 2011
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- Prisoners’ problem 6 June 29, 2011
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- A non-associative “group” March 21, 2011
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# Monthly Archives: October 2010

## More Chessboard

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 chess board
3 Comments

## Prisoners’ Problem 5

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 Prisoners' problems
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## Incomplete Chess Board

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 chess board
2 Comments

## Map Colouring Problem And Compactness

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
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## Poisoned Bunnies

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

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