Category Archives: Recreation

Time Limit: One Minute!

Posted on August 17, 2011 by Vadim Kulikov

I found this lovely geometrical riddle in Martin Gardner’s book “My Best Mathematical and Logic Puzzles”. The most lovely thing about it is that Gardner gives a time limit: one minute! So, now draw out your stopwatch and read the … Continue reading →

Posted in Geometry, Mathematics, Popular, Recreation, Wednesday Problem | 11 Comments

Walks on Planets

Posted on July 6, 2011 by Vadim Kulikov

My gps-equipped radiowave controllable robot Lori is somewhere on the surface of Earth. I order her to drive 100 miles South and she obeys. Then I order her to drive 100 miles West and she obeys. Then I order her … Continue reading →

Posted in Geometry, Mathematics, Popular, Recreation, Wednesday Problem | 7 Comments

Prisoners’ problem 6

Posted on June 29, 2011 by Vadim Kulikov

Three prisoners meet a guard. The guard says: I have hats with me, two of which are black and the others are white. The prisoners ask: “How many hats there are all together?” He says: “It’s a secret!”. The guard … Continue reading →

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

Doodling with Fractals and Persistent Worms.

Posted on January 2, 2011 by Vadim Kulikov

Suppose we have a rubber line of length 1 m and a worm at the other end. The worm moves 10 cm in a minute and its goal is to reach the other end moving along the rubber line. However … Continue reading →

Posted in Combinatorics, Geometry, Mathematics, Recreation | 1 Comment

Splitting A Rectangle

Posted on November 17, 2010 by Vadim Kulikov

Find all ways to cut a rectangle into two connected pieces of equal area so that they can be rearranged to get a new rectangle with different dimensions (side lengths) than the orgininal one. I already know countably many ways. … Continue reading →

Posted in Geometry, Mathematics, Recreation, Wednesday Problem | 2 Comments

A Year Problem

Posted on November 3, 2010 by Vadim Kulikov

There are more year problems than years. But since I have been pondering on this particular one, I will present it here. You are allowed to use +, -, / and * (plus, minus, division and multiplication) signs and bracketing. … Continue reading →

Posted in Algebra, Combinatorics, Mathematics, Recreation, Wednesday Problem | 12 Comments

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

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

Euler’s Riddle

Posted on June 16, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. I found in a recreational book the following riddle attributed to Leonard Euler. The book gives a clumsy solution involving solutions of quadratic equations, a lot of fractions and half a page of … Continue reading →

Posted in Algebra, Mathematics, Recreation, Wednesday Problem | 2 Comments

How To Find Your Way Out of Woods

Posted on June 9, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. A lumberjack got lost in a forest. He knows that the area of the forest is S and that there are no meadows in the forest. Show that he can get out from … Continue reading →

Posted in Geometry, Mathematics, Recreation, Wednesday Problem | 3 Comments

If You Beg For Money, You Might End Up Doing Math

Posted on May 5, 2010 by Vadim Kulikov

Yesterday I was walking around with my friend in a market hall. Two girls of age 15 asked us whether we could give them 40 euro cents. It is about $0.6. We asked them what could we gain in response. … Continue reading →

Posted in Education, Meta, Recreation, Wednesday Problem | 3 Comments

Prisoners’ problem 4

Posted on April 28, 2010 by Vadim Kulikov

The rules are as in the previous problem, but this time there are only 100 prisoners. How should they do so that 50 of them certainly survives? 3/5

Posted in Combinatorics, Mathematics, Recreation, Wednesday Problem | Tagged | Leave a comment

Prisoner’s problem 3

Posted on April 21, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. There are infinitely many prisoners in a prison. The prisoners are taken to the yard and everyone is given a hat which is either black or white. No one knows the colour of … Continue reading →

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

Prisoner’s problem 2

Posted on April 14, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. Consider a prison with several millions prisoners. The head of the prison arranges the following challenge to the prisoners. One prisoner at a time will be called to a room with a lamp. … Continue reading →

Posted in Mathematics, Probability, Recreation, Wednesday Problem | Tagged | 2 Comments

Prisoner’s problem 1

Posted on April 7, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. We are going to have several prisoner problems! Better solve them before you end up in jail. There are 2010 prisoners in the prison. One day the chair of the prison gathers the … Continue reading →

Posted in Combinatorics, Mathematics, Recreation, Wednesday Problem | Tagged | 5 Comments

Andre’s Reflection Method

Posted on March 20, 2010 by Vadim Kulikov

I promised to post something about random walks. I learned the content of this post while listening to Vilppu Tarvainen’s bachelor’s degree talk and I consider it is quite cute. Let us consider a one dimensional random walk: formally it … Continue reading →

Posted in Combinatorics, Mathematics, Probability, Recreation | 1 Comment

How Many Are True?

Posted on March 10, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. At most 1 statement of this post is true. At most 2 statements of this post are true. At most 3 statements of this post are true. At most 4 statements of this … Continue reading →

Posted in Logic, Mathematics, Recreation, Wednesday Problem | 1 Comment

Sorry I Am Late

Posted on February 26, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. How many of the statements below the line are true? 2/5 ———— This post was not published on Wednesday 24. February 2010 There are at least 2 true statements in this post (after … Continue reading →

Posted in Logic, Recreation, Wednesday Problem | 3 Comments

Pinocchio Is Omnipotent

Posted on February 19, 2010 by Vadim Kulikov

Please visit my new website at www.vadimkulikov.org to find more about mathematics, science, cognitive science and art!  

Posted in Logic, Mathematics, Philosophy, Recreation | 15 Comments

More Tricks With Triangulations

Posted on February 17, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. I learned this riddle from Sergei Chmutov. It is also a problem concerning triangulation and sharp angled triangles. Suppose we have a triangulated regular polygon with odd number of edges. The vertices of … Continue reading →

Posted in Geometry, Mathematics, Recreation, Wednesday Problem | Leave a comment

Stable Marriages

Posted on February 14, 2010 by Vadim Kulikov

Suppose n men and n women survived after a spaceship crush on a planet orbiting Alpha Centauri. They happen all to be heterosexuals and all single (or their partners died in the crush). Each man then ranks women in order … Continue reading →

Posted in Combinatorics, Mathematics, Recreation | Leave a comment

Triangulation

Posted on February 10, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. In the last week’s many in one post I explained what is a triangulation. Can you triangulate a square using only sharp angled triangles (i.e. triangles whose all angles are <[tex]\pi/2[/tex])? For example … Continue reading →

Posted in Geometry, Mathematics, Recreation, Wednesday Problem | Leave a comment

The Coin Placing Game.

Posted on January 27, 2010 by Vadim Kulikov

See the Wednesday Problem’s vague rules here. Some games again. According to Sam, from whom I heard this riddle, it divides people into cathegories i) those who realize the answer immidiately and ii) those who think quite long about it. … Continue reading →

Posted in Games, Recreation, Wednesday Problem | 6 Comments

How Old Are The Kids?

Posted on January 20, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. This is quite famous. But maybe you haven’t heard it yet: A math student goes to a party organized by her supervisor. The student asks: How many daughters do you have? And the … Continue reading →

Posted in Combinatorics, Recreation, Wednesday Problem | 2 Comments

The Monk

Posted on January 13, 2010 by Vadim Kulikov

Please comment your solutions, questions and remarks.. The posts have been a bit advanced lately. Let us lighten the atmosphere by this riddle which admits a simple solution, though mathematicians tend to use calculus in solving it: An Indian monk … Continue reading →

Posted in Calculus, Recreation, Wednesday Problem | 2 Comments

Joulupukki Is Fair: Your Christmas Riddle

Posted on December 23, 2009 by Vadim Kulikov

Please comment your solutions, questions and remarks.. Joulupukki came to a kindergarten. He had some number of candies to give to the children. He saw that there are more boys than girls and that he could divide the candies evenly … Continue reading →

Posted in Mathematics, Recreation, Wednesday Problem | Leave a comment

The Game Discrete

Posted on December 20, 2009 by Vadim Kulikov

Inspired by my post about tic-tac-toe I want to introduce a game. It is played on a 3x3x3 grid or equivalently on a 9×3 grid:

Posted in Combinatorics, Games, Mathematics, Recreation | Leave a comment

Handshaking Lemma

Posted on December 16, 2009 by Vadim Kulikov

Please comment your solutions, questions and remarks.. This one I learned from Sam Hardwick. Show that the number of those, who have shaken their hands with others an odd number of times, is even. Level 1/5 P.S. This lemma has … Continue reading →

Posted in Combinatorics, Recreation, Wednesday Problem | 2 Comments

Ants

Posted on December 9, 2009 by Vadim Kulikov

Please comment your solutions, questions and remarks.. This funny riddle I heard from Marcin Sabok. There are n ants on the unit interval, [0,1]. Each has a direction, left or right. In the picture above there are three ants and … Continue reading →

Posted in Mathematics, Recreation, Wednesday Problem | Leave a comment

The Chocolate Game

Posted on December 2, 2009 by Vadim Kulikov

Please comment your solutions, questions and remarks.. I heard this from Lauri Hella, but he doesn’t remember from whom he heard this. The game is played between two players as follows. There is an [tex]n\times m[/tex] bar of chocolate on … Continue reading →

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

Tic-tac-toe And A Non-Constructive Proof

Posted on November 30, 2009 by Vadim Kulikov

Usually the game tic-tac-toe is played on an infinite board (i.e. 30 times 40 or something). The two players draw X:s and 0:s to the squares of a notepad paper. Player 1 (beginner) is the X-drawer and the Player 2 … Continue reading →

Posted in Combinatorics, Games, Mathematics, Ramsey Theory, Recreation | Leave a comment

Erdös and the individual property of dimensions 1 and 2.

Posted on November 26, 2009 by Vadim Kulikov

Some time ago I read a biography of Paul Erdös titled ‘my brain is open’ written by Bruce Schechter. The book contains some popular exposition of math. As a biography the book is good, but much of the mathematics and … Continue reading →

Posted in Geometry, Mathematics, Recreation | Leave a comment

A liar’s paradox

Posted on November 26, 2009 by Vadim Kulikov

I will hereby argue that I am the Pope. Consider the following sentence: If this sentence is true, then I am the Pope. It is an implication, i.e. a sentence of the form [tex](A\to B)[/tex], where A is “this sentence … Continue reading →

Posted in Philosophy, Recreation | Leave a comment