# matchstick problem

10 messages
Open this post in threaded view
|

## matchstick problem

 ---  "You don't have to believe in God, but you should believe in The Book." -Paul Erdős
Open this post in threaded view
|

## Re: matchstick problem

 same problem.... M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
Open this post in threaded view
|

## Re: matchstick problem

 This post was updated on . Maybe this will help? I really don't think that its possible to solve this question in a way that isn't tedious. Edited: Try this link instead. You will have to scroll down a tiny bit to the part where it says "Square Game".
Open this post in threaded view
|

## Re: matchstick problem

 just remember that a player is allowed to pick 1/4/9/16 and his aim is to leave zero sticks for the other player. then make a tree with possible combinations of moves and you'll see a lot of them get eliminated. it isn't very tedious. for example u know to start with that if player 1 picks 1 or 16, player 2 can make choices in a way that he wins, so work it out only with 4 or 9 in the first stage.
Open this post in threaded view
|

## Re: matchstick problem

 In reply to this post by Do bats eat cats? Thanks you so much Do Bats eat cats...What I was looking for...You just provide the link for that.. Thanks vasudha for your inputs but don't you think it takes time to make the tree n there is still chances that after making the tree you end up marking a wrong answer(due to mistake while making tree).....Just have a look the link provide by Do Bats eat cats...I can't think of a simple method than this.... M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
Open this post in threaded view
|

## Re: matchstick problem

 What? Do we need to memorize this pattern: LWLWW ... ? ---  "You don't have to believe in God, but you should believe in The Book." -Paul Erdős
Open this post in threaded view
|

## Re: matchstick problem

 Sinistral, I hope you checked the second link and not the first. Just draw a table and think of this from the point of view of the first player. If there are 1, 4, 9 and 16 matchsticks, the first player will win. Thus, these are the winning positions. Mark them "W". Note that 2 is a losing position (the only possible play is 2 → 1 → 0). This means that if player 1 can force player 2 choose from a pile of 2 matchsticks, he is guaranteed to win. Player 1 can leave 2 matchsticks if he gets to choose from either 3, 6 or 11 matchsticks. So, these are winning positions for player 1 too. Moving like this you can find all the winning positions yourself, if you know the losing positions. The problem is now finding all the losing positions. You will find that the smallest number that is still unmarked in your table has to be a losing position. So, far it is the number 5 (note that all permissible moves from 5 lead to winning positions for the second player). So, 6, 9, 14 are winning positions as well, and so on.
Open this post in threaded view
|

## Re: matchstick problem

 Earlier, I went through that link in such a rush... thanx a lot. :) ---  "You don't have to believe in God, but you should believe in The Book." -Paul Erdős