On the other hand, L and J placements will add 3 squares to odd-numbered columns and 1 square to even-numbered columns, or vice-versa. Vertical I placements will exclusively add to either odd- or even-numbered columns, but again the difference between odd and even changes by a multiple of 4. S, Z and horizontal I placements will add 2 filled squares to both odd- and even-numbered columns which will not affect the difference. In both cases, the difference between squares in odd- and even-numbered columns is a multiple of 4. Since our rectangle must contain a multiple of 4 squares, it must have an even amount of columns or its height must be a multiple of 4.

To see this result, we compare the number of covered squares in odd-numbered columns (columns 1, 3, 5, 7 and 9) and even-numbered columns (columns 2, 4, 6, 10). To fill a rectangle, you will always need an even number of L, J and vertical T placements (if you count all those placements together, then it must add up to an even number).The J placement clears the third row with an odd number of empty cells below (and above). Clearing 2 or 4 lines directly above each other will not have any effect either (horizontal T-Spin Double or Tetris). line clears at the bottom or very top) will not have any effect. On the other hand, single line clears with an even number of empty cells below (e.g. Summarizing: Single line clears with an odd number of empty cells below the cleared line will have the same effect as placing a T-Piece regarding parity. Also, the imbalance of covered white and black squares does not exceed 2, in which case a line clear affecting parity will have the same effect on the (im-)balance as placing a T piece. For Perfect Clear setups, we have an even amount of filled squares, so an odd number of filled squares above a line clear is equivalent to an odd number of squares below the line clear. Usually, line clears will affect parity, if an odd number of filled squares falls down an odd number of rows. This means that you need an even number of T pieces, if you do not regard line clears. To completely fill a rectangle, you need to cover the same amount of white and black squares in the end. On the other hand, A T piece will cover 3 white and 1 black squares or 1 white and 3 black squares. Parity: If you lay a checkerboard pattern over the playfield (alternating white and black squares), then all pieces but the T piece will cover 2 white and 2 black squares when placed anywhere on the pattern.After an odd number of cleared lines, at least ½ piece worth of filled squares will remain in the playfield (amount of filled squares divided by 4 will give a rest of 2). Each cleared line subtracts as many filled squares from your playfield as 2 ½ pieces will add. Without incoming garbage, you can obtain a Perfect Clear only after an even amount of total cleared lines.Some theoretical results about filling rectangles that can be useful knowing in regards of Perfect Clears:

Perfectly clear 2