László Kozma

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Color-changing links

Browser bookmarks are difficult to synchronize if you use more than one computer, possibly running different OS's and browsers. The only way to have your links accessible all the time is to keep them online. For me, social bookmarking sites were an overkill, as I only need a simple page listing all the links, with a basic interface to add/remove items. I can set this site to be my startup page in all browsers. A wiki would do, but while I'm at it, why not add some visual extravaganza. The red color of the links shows how often they are clicked, compared to other links in the same group. This way the important ones are more easily found, and the ones never used can be spotted if needed. Additionally, the color of a link decays with time, so links that haven't been clicked for a long time slowly change back to black. The green component shows how long ago the link was added.

In the spirit of eating one's own dogfood, my bookmarks are organized this way. If you want to create a similar page of your own, I'll host it for free. The interface for editing your page might seem strange at first, but it's easy to use. You can enter scripts to execute more commands at once. If your pass-code is foo, you can add a category and a link to it, with the following script:

• Create your own page
  
  
• Visit my links
  
  
• Drop me a mail if you have a suggestion on how to make this service more usable.
  

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Paper/pencil game

One of these days, I came up with the idea for the following game:
Two persons play on some rectangular checkered board. Players alternate in putting a piece in a free square (just like in Go). If played on paper, they can just mark a square in every step. It is not allowed to choose a square that has any of its neighbours (out of the 8 or less) already taken. If a player can't put a piece anywhere, he loses.
Mathpuzzle featured it under the ominous name "Obliteration Game".

				O
	X
				O
				X

Since the gameplay is completely deterministic, one of the players must have a winning strategy for each board size. For example, the first player wins on a 3*3 board, but loses on 2*4. For smaller boards it's trivial to figure out who wins, but on a large board this can lead to a lot of computation. As a puzzle, you can find who wins on 4*4, 4*5, 4*6, 5*6, and 6*6.

I haven't seen the game in this exact form, but doing some research, I found several existing games that are very similar to it. The 1*n version is known as Dawson's chess, it can be played online here, and a game called Regio already exists, which is almost the same, the only difference being that in Regio only the 4 direct neighbors are considered, instead of 8.

More information about the game...

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Knight's tour game

This two-player game is played on a checkered board of arbitrary size (larger than 3*3). The first player chooses a starting position, where he places a knight. The second player makes a move, according to the regular chess-rule of knight movement. Then first player makes a move, then the second again and so on (the moves are made with the same knight). Every field on which the knight has jumped (including the starting position) are marked, and it cannot jump on a marked position again. The player who cannot move loses.

	0
		4	1
	2
			3

(0 is the starting position, the numbers show the order of moves in an example game)

To my knowledge, this game hasn't been described before, if you know otherwise, I'd be glad to hear about it. It is interesting to find out which player has a winning strategy for each board size. On a 4*4 board for example, the second player can always win. In the general case I am not aware of any simple solution. This game is related to the Knight's Tour problem on a chessboard.

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