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One Piece Tetris (Posted on 2007-12-19) Difficulty: 4 of 5
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
#                                  #


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.

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (3 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: case 4Charlie2007-12-20 16:39:50
case 4Hugo2007-12-20 14:18:37
SolutionCases 1 - 3Charlie2007-12-19 19:00:59
Hints/Tipsre: a way to play around with this -- pentominosCharlie2007-12-19 14:38:59
Hints/Tipsa way to play around with thisCharlie2007-12-19 14:23:17
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