One Piece Tetris (Posted on 2007-12-19)

A typical game of Tetris has 10 columns and 7 pieces. Consider a variation with fewer columns and only one piece, which repeats indefinitely.

For some pieces and column widths it is trivial to see that an infinite game is possible. For example the I tetromino with any column width or any other of the tetrominoes with an even column width.

For other pieces, an infinite game is possible, but not trivially so. Consider the T tetromino in three columns, an infinite game is possible by following a pattern: The first piece is horizontal with the stem of the T pointing down. The second piece is vertical, with the stem of the T pointing to the right and the T is pushed to the left edge. The third piece is vertical, with the stem of the T pointing to the left and the T is pushed to the right edge.

For each piece and number of columns listed below, find a strategy for each which allows for an infinite game:

1.                               2.
### in three columns             ### in four columns
#                                 #
                                  #
								  
3.                               4.
### in four columns              ##### in five columns
#                                  #
#

-----------------------------------------------------

Notes:
1 - Using the reflection of an asymmetrical piece is not allowed.
2 - Use classic gravity: when a row is filled, it is removed and all rows above move down, but no fragments of one partially filled row fall into another partially filled row.

	Submitted by Brian Smith
Rating: 4.0000 (3 votes)
Solution:	(Hide)
My solutions are below. To save space I tipped each column on its side. For some pieces there are two sets. The first set(start) is a few pieces used to setup a grid which repeats with the second set(repeat). Charlie has solutions for the first three pieces here. Hugo has a solution for the fourth piece here. ### in three columns # start +------------- | A BBB | AA B | A +------------- repeat +--------------- |XXX B CCC |XX A BB C | AAA B +--------------- ### in three columns # +---------------------- | CC DD EE FF | AAA B C D E F | A BBB C D E F +---------------------- ### in four columns # # +-------------------------------------- | AAA CCC GGG H | A B C D EEE F G H | A B C D E F G HHH | BBB DDD E FFF +-------------------------------------- ### in four columns # # start +--------------------------- | AAA CCC E | A B C D EEE F | A B C D E FFF | BBB DDD F +--------------------------- repeat +------------------------------------- |X AAA CCC EEE G |XX A B C D E F GGG H |XX A B C D E F G HHH | X BBB DDD FFF H +-------------------------------------

	Subject	Author	Date
	re: case 4	Charlie	2007-12-20 16:39:50
	case 4	Hugo	2007-12-20 14:18:37
	Cases 1 - 3	Charlie	2007-12-19 19:00:59
	re: a way to play around with this -- pentominos	Charlie	2007-12-19 14:38:59
	a way to play around with this	Charlie	2007-12-19 14:23:17