So I came across this flash game called Znax in my bout of boredom today.


The game's a bit of an interesting twist on the typical click-on-colored-boxes "meme" in Flash games. Rather than simply clicking blindly on groups of similarly colored boxes, you instead have to find 4 similarly colored boxes that form a rectangle on the playing grid. When you select 4 such boxes, you clear all boxes that lie within the enclosing rectangle formed by the selected boxes. Any boxes that disappear get replaced with new boxes having random colors. There are only four different colors: red, yellow, green, and blue.

It's not a terribly exciting game, and it's not really even a game that held my attention for that long. What did get me thinking, though, is the following question:


If you can prove that there is always a legal move, or if you can provide a counter-example board showing that it's possible to get completely stuck, I'd be interested in knowing. It's possible that this is a brain-dead simple question, but it's nearing 3 AM in the morning, so... give me a break. :P

[UPDATE: I believe I have answered my own question. I don't think it's that obvious, though, and I think it's fun to make others figure things out.]