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Guest Message by DevFuse
 

witzar

Member Since --
Offline Last Active Jan 19 2015 09:32 AM
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#341304 LCD Watch

Posted by witzar on 13 December 2014 - 03:35 PM

Spoiler for

 

Edit:

Spoiler for oops


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#341068 Covering chessboards with dominoes

Posted by witzar on 14 November 2014 - 12:25 PM

Spoiler for 3


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#341067 Covering chessboards with dominoes

Posted by witzar on 14 November 2014 - 12:04 PM

Spoiler for 2


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#341066 Covering chessboards with dominoes

Posted by witzar on 14 November 2014 - 11:38 AM

Spoiler for 1


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#341065 Covering chessboards with dominoes

Posted by witzar on 14 November 2014 - 11:24 AM

Spoiler for 4


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#340921 Paradise anyone?

Posted by witzar on 02 November 2014 - 03:46 PM

Spoiler for


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#340770 Removing pawns - the game

Posted by witzar on 25 October 2014 - 12:41 PM

Here is the simple game I've invented (if someone invented it before, then I'm not aware of it):

 

A pawn is placed on every square of m*n chessboard.
Two players take alternate turns removing pawns.
On each turn, a player removes one or more pawns.
All pawns removed in a single turn have to be taken from the same row or the same column.
The player who cannot make a move loses (alternatively: the player who takes the last pawn wins).

Let's call the player who begins the "first player" and the other one the "second player".

Which player (the first or the second) has a winning strategy depending on the chessboard dimensions?
 

PS The game can be played on more interesting boards. Just draw some number of crossing lines

on a sheet of paper and place a pawn on each point of intersection of the lines.

The pawns removed in a single turn should come from a single line.

I've tried to play this game on the pentagram (the star: five lines, ten points/pawns) with my 9 years old daughter.

It was fun. Determining which player wins was even bigger fun.


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#340514 Random points on x-axis

Posted by witzar on 07 October 2014 - 05:47 PM

Asking about probabilities makes no sense unless there is a probability distribution.

Unfortunately there is no reasonable distribution on R+.

But an obvious distribution exists on interval [0,x], where x is any positive real number.

One thing we can do in such case is to try to solve the problem for [0,x] and then see

if the solution has a limit when we go with x to infinity.

With this approach it's obvious that the probability we look for equals 0.5 for every x,

so obviously it's limit is also 0.5 when x goes to infinity.


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#335048 i am thinking of a number...

Posted by witzar on 08 August 2013 - 05:54 PM

Spoiler for


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#332897 Probability of a rope cut exactly in half, in a single slice

Posted by witzar on 10 June 2013 - 04:37 PM

there are only three possibilities of this experiment after the cut.
 
1. Left peice is bigger
2. right peice is bigger
3. left peice = right peice
 
so the probability he calculated is 1/3

 

It would be true, if all three possibilities were equally probable.

Which is not the case.


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#330214 a simple pattern.?!

Posted by witzar on 01 April 2013 - 01:59 PM

Spoiler for obvious formula for n-th term

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#328252 Matryoshka

Posted by witzar on 14 February 2013 - 11:16 AM

Spoiler for all solutions


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#328131 1966

Posted by witzar on 08 February 2013 - 01:59 PM

Spoiler for Solution


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#327871 Rubber Stamping Dots

Posted by witzar on 31 January 2013 - 05:19 PM

there are 3 paths for all square roll..G N R, which way you pass?

Spoiler for I can pass...


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#321223 All the people like us are We, and everyone else is They.

Posted by witzar on 05 July 2012 - 12:47 PM

the difference may be infinitesimally small but it exists...


1. The difference of two real numbers numbers always exists and is also a real number.
2. A real number cannot be "infinitesimally small".
3. Please don't answer "thanks for the explanation, but I'll stick to... " :)
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