BOOM! Perfect Clear for Mr. T

Question

In Tetris, Mr. T loves performing Perfect Clears, when a piece clears all lines in the playing field. As you might guess, when it comes to tetriminos, he has a personal favorite: the undeniably cutest O piece. But a Perfect Clear using only O pieces is not terribly exciting, so Mr. T wants to use his second favorite tetrimino: the T piece.

Starting with an empty field, can Mr. T achieve a perfect clear using only T pieces? If so, how fast can he pull it off? Mr. T is not easily persuaded by smooth talk, so please justify your answer with a convincing argument.

The standard Tetris field has ten columns. The T tetrimino has three minos adjacent to a central mino in a T shape, as shown below.

OOO
 O

@Glorfindel Just a bit of humor and a small reference to a character from a recent Tetris game. :) — noedne, May 01 '19 at 13:38
n̶o̶o̶,̶ ̶s̶c̶h̶e̶z̶o̶ ̶i̶s̶ ̶t̶h̶e̶ ̶c̶u̶t̶e̶s̶t̶ ̶b̶o̶y̶ — athin, May 01 '19 at 14:18

Glorfindel · Accepted Answer · 2019-05-01T13:31:05.500

21

It can be done with

10 T tetrominoes (if you allow rotation – this is necessary because otherwise it's not possible to get as much 'squares' in the first row as in the second, which is a prerequisite for clearing the field).

Some explanation:

First, drop the three yellow ones and the orange one on the left (first picture); this clears the bottom line.
Then, drop the three light blue ones and the dark blue one on the left (second picture); this clears the second line.
The final two tetrominos (green) can be dropped (third picture) to clear the final two lines.

Since

the number of columns (10) is not divisible by 4, the total number of rows must be even. I don't see a possibility to do it in two rows, you'll need 'vertically' placed tetrominos and those always need three rows.

edited May 01 '19 at 13:31

answered May 01 '19 at 13:19

Glorfindel

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That's a great answer. I wasn't anywhere close to that. – Jaap Scherphuis May 01 '19 at 13:30
"you'll need 'vertically' placed tetrominos" -> theorem. I managed to prove it. – Joshua May 01 '19 at 15:37
1

The first spoiler block contains some reasoning why they are needed. – Glorfindel May 01 '19 at 15:39

score 6 · Answer 2 · edited May 01 '19 at 18:18

6

A simple solution involves

10 T Tetrominos.

Stack the first five arranged the same direction (on the side of the T with the bottom facing either left or right. In my example, the bottom is facing the right). This eliminates the second row (shown with Xs through them). Next, flip the T 180 degrees so the bottom is facing the other direction and fill the gaps as such. This should immediately eliminate rows 3 and 4. The squares in row 5 fall down to row 1 and the sum of those squares eliminates the final row.

edited May 01 '19 at 18:18

noedne

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answered May 01 '19 at 18:17

Quinn

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Welcome to Puzzling! I have placed parts of your answer in spoiler tags to avoid spoiling other solvers. Please take the tour! – noedne May 01 '19 at 18:19
1

Regarding your solution, I should have specified that naive gravity was in play, as in most games. This certainly works under cascade gravity that some game modes have. – noedne May 01 '19 at 18:21

score 2 · Answer 3 · edited Jul 03 '20 at 15:16

2

This is the same as Glorfindel's solution but using a much more compact visualisation:

Note that pieces 9 and 10 become connected after piece 8 clears a middle line.

edited Jul 03 '20 at 15:16

Quintec

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answered Jul 03 '20 at 09:43

happystar

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BOOM! Perfect Clear for Mr. T

3 Answers3

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