jason_t
03-29-2005, 01:29 PM
Here's a two-way infinite chessboard with a blue dot in its lower left corner.
http://i3.photobucket.com/albums/y73/jason_t712/dots1.jpg
The board streches infinitely far up, and infinitely far to the right.
The idea is to obtain a configuration with no blue dots behind the bold black line. You move pieces as follows. If a square with a blue dot in it has the square above it and to the right of it free of blue dots, then you can remove the blue dot from the original square and place blue dots in the squares above and to the right of the original square. Therefore
http://i3.photobucket.com/albums/y73/jason_t712/dots2.jpg
becomes
http://i3.photobucket.com/albums/y73/jason_t712/dots3.jpg
Your goal is to make such moves over and over to free the region behind the bold line of blue dots.
http://i3.photobucket.com/albums/y73/jason_t712/dots1.jpg
The board streches infinitely far up, and infinitely far to the right.
The idea is to obtain a configuration with no blue dots behind the bold black line. You move pieces as follows. If a square with a blue dot in it has the square above it and to the right of it free of blue dots, then you can remove the blue dot from the original square and place blue dots in the squares above and to the right of the original square. Therefore
http://i3.photobucket.com/albums/y73/jason_t712/dots2.jpg
becomes
http://i3.photobucket.com/albums/y73/jason_t712/dots3.jpg
Your goal is to make such moves over and over to free the region behind the bold line of blue dots.