The Grid Game

This is from a website called deviantART.com


It's called the Grid Game. It's a neat little game, definitely worth a couple minutes of your time. Click here to actually play it. I just wanted to show off my high score.

I got this off of the Troupe list (special thanks to Ketner for letting us know of it's existence). For those of you who don't know, the Troupe is an improv group I was involved with at college. Since we attended an engineering university, it was nice to exercise the other half of our brains doing wacky and "organic" stuff.

Anyway, with creativity, mathematics and lots of time to think inside (damn snow), you get people who can think like this:

I'm pretty sure infinite loops are not possible.

Each piece is only rotated 90 degrees per activation and the two activation edges are only 90 degrees apart. If you look at each of the 4 corner pieces, there is an orientation which causes the tile to be dead: when the two activation edges face the edge of the board.

So the 4 corner pieces can be removed from play through random processes. Furthermore, each time one of these four pieces has been removed from play the two pieces adjacent can now be removed from play in the same manner. This process continues: each dead tile making at least one other tile eligible for deadness. And each tile eligible for deadness will become dead within three touches.

This isn't a complete proof. You also need to show that a sub-group (NxN) cannot continue forever without interacting with a tile outside of the subgroup. It is obvious for a 1x1, then show it for a 2x2 and prove that if it is true for an NxN, then it must be true for an (N+1)x(N+1). You wouldn't even need to use the dead tile observation.

That's from my pal Mikey. This is the same guy who giggled with me and another friend for half an hour over the phrase "steel blue." (You had to be there.)

Oh, and you might be wondering how I got all the little quarter-circles to face the same way in the picture up there. It's not hard. Play the game a couple times and you'll see why. It's neat. After a while you can see the little circles move across the board in waves. There's probably a configuration you can use to get them all to move across the board from one corner to the other in one pass and then stop, but I don't feel like looking for the answer right now.

So! Here's to Ketner and Mikey for another seven minutes of my day delightfully wasted.