I hope this problem is not as hard as I think it is. :)

Imagine that you are playing a game of Tetris. However, one of your game console's buttons has malfunctioned, leaving you unable to rotate your pieces. What is the maximum number of tetrominos you can drop before you lose?

NOTE: The 7-bag rule applies; however, for simplicity, let us disregard the tetrimino holding feature. Also, the Tetris matrix is ten blocks wide and 20 blocks tall.

#MathProblem

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Great question, my friend. As a Tetris Lover, I'm really trying to produce an answer to this problem. As you see, the pieces always spawn with their flat side down. Its not hard to see that there are only 2, 3 and 4 mino's long flat sides. That said, the key technic is to count the number of one-spaced holes that remain in the field after one line clear. I'll use the fumen to ilustrate my point:

http://tinyurl.com/ac6cqn2 (Just click "next" to advance the frames)

As you can see, there are two one-spaced holes and,obviously, no piece can fit in there. Well, thats just my inicial thought hahaha But I think I'm on the right way.

Now, I think I'll discover wich piece sequencies leave the lowest number of odd-spaced holes (as 3 and 5 holes long gaps are stil hard to deal with)

Good luck for ya! ^^

Hugo Terceiro - 8 years, 3 months ago

Found a beautiful pattern that maybe produce the right answer. I'll just leave the fumen here so that you can see what I am doing. Maybe tomorrow I can put some equations up to back up my work. Now I'll go get some sleep hahaha

Fumen ~ Tetris Pattern

Hugo Terceiro - 8 years, 3 months ago

thanks, i've tried doing this in actual games several times, and I got as far as 60 lines before topping out. :) trying to avoid odd-spaced holes does help.

Francis Gerard Magtibay - 8 years, 3 months ago

well, it depends on what pieces come. imagine u get only the pieces that have four blocks in a straight line, then ur matrix will be filled by 50 pieces, but if any single piece of them is not the piece ive mentioned above, then the number of pieces will decrease. so the maximum number is 50 pieces, after that u will lose

Ayush Alankar - 8 years, 3 months ago

Actually, that can't happen. We are assuming that the 7-bag rule counts, i.e, you will receive one piece of each kind in blocks of seven, at random. That said, you can receive 4 O blocks, but at most two. Example: Bag 1 (I L J Z S T O) Bag 2 (O I J L Z T S)

The pieces will spawn in that sequence and you will receive Two straight O's.

Hugo Terceiro - 8 years, 3 months ago

that's why we apply the 7-bag rule, as in an actual game of Tetris. please see Hugo's comment. :)

Francis Gerard Magtibay - 8 years, 3 months ago

Sorry, I don't play Tetris.

Zi Song Yeoh - 8 years, 3 months ago

What is Tetris?

Tan Li Xuan - 8 years, 3 months ago

Tetris

Zi Song Yeoh - 8 years, 3 months ago

A game

Zi Song Yeoh - 8 years, 3 months ago

This question's too hard for me :D

Tan Li Xuan - 8 years, 3 months ago

 50. That's the number of blocks required to fill in the whole grid.

Amey Desai - 8 years, 3 months ago

We're gonna consider line clearing of course. If you make a horizontal line of 10 tetriminos they disappear, thus providing more space. :)

Francis Gerard Magtibay - 8 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$