Entertainment

[peachy]

I have been on medical leave for a while and will be for a couple months more. Could y'all please give links to some fun puzzles, games, brain teasers or other stuff to get my mind off my worries. Thx!

[kenberg]

Here is a fairly easily stated problem that I don't know the answer to. It has a little background that I could explain if needed.

 

Background:

Simple Nim is played as follows:

There are two players. On the table there are several stacks of tokens. Players alternate making moves. A move consists of taking as many tokens as you like (but at least one token) from one of the stacks. The person who takes the last token wins.

The solution to this game is well-known. I could explain, or you could find it on the web. (Solving this game means providing a reasonably succinct description of the winning positions and the winning moves.)

 

I believe that the late Richard Guy proposed the following variant. Play NIim as above except that once, at any point in the game BEFORE the last token is taken, one of the players may elect to pass (ie take zero tokens). The game ends when the last token is taken (no pass allowed after that) and the person taking the last token is the winner. After one of the players elects to pass, the paass option is no longer available to either player.

 

Note that, for example, a three stack game allowing one pass is NOT equivalent to standard Nim simply adding one more stack of height one. That extra stack would be available as a move after the three stacks have been deleted. but we do not make the pass available after the three stacks have been deleted. I mention this because a friend suggested that solution after I, perhaps too vaguely, described the game to him.

 

 

To get you started:

 

In two stacks with standard Nim, the losing positions are those where the heights are equal. Any move by the person on play makes the heights unequal, and the response is just to even them out.

 

In two stacks with a pass allowed, you can get the idea by considering stacks of heights 2 and 1. This is a losing position. If the first player takes all of either stack, the response is to take the other stack. If the first player takes one from the tall stack, leaving two stacks of heights one, the response is to pass. If the first player passes, the response is to take one token from the taller stack. A little thought and/or exploration and you will discover the winning and losing positions for two stacks.

 

Note that heights 2 and 3 is a winning position: Take 2 from the larger stack, handing your opponent the losing (2,1) position.

 

I have been meaning to try to work out the general patter for an arbitrary number of stacks but I have not done so. This might be quite difficult, I am not claiming that of course I can do it whenever I choose to. Maybe someone else has done it. Maybe not.

 

 

Being retired means only having to try problems if you feel like it. :rolleyes:

[Jlall]

www.addictinggames.com

[diana_eva]

http://www.thestylemachine.com/metele/

[Fluffy]

http://www.58works.com/

 

escape games are fun to play and if you get frustrated it is easy to get the solution online :), I introduced my girldfriend to them and now she is addicted.

[655321]

http://www.jigidi.com/

[y66]

You might like NPR's Sunday Puzzle or the Car Talk Puzzler.

 

Wait wait ... don't tell me is a fun radio quiz show.

 

In the other stuff category, something I enjoy as a diversion is hanging out at the local park watching a ball game or just people watching.