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I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch.

Well, at least I learned a lot about this puzzle type, and you get a Valentine's card as an answer for the main challenge.

The sixth and final Z (the one that appears separately from the initial burst) is the one on the top left. The rest should be more or less self-explanatory, so I didn't add any extra borders that might affect the artistic merit of the solution.

POST MORTEM/SCRIPTUM

I had misunderstood OP's piece order, but no worries, everything still works, and the heart shape only needs one easy tuck (piece number 5) that's definitely doable in Classic Tetris too.

(My apologies about the eye-sore. Why can't I re-spoilerize that picture..)

Method:

There are a couple of main constraints (as far as I noticed) in the puzzle:

1. Whenever you cut off an empty area, and don't have a plan to reconnect it (by making rows disappear), its size must be divisible by four.
2. The T piece's position is restricted by parity: if you imagine a checkerboard pattern on the background, then every piece except the T will contain 2 dark and 2 light squares. The greyed-out squares are correctly imbalanced to take the T piece into account, but half of the positions on the board would increase the imbalance, instead of bringing it back to zero.
3. the number of extra Zs must be divisible by 5: the number of extra squares they contain must be divisible by the line length. So 5 extra Zs is the absolute minimum.

Apart from those, it was mostly just playing Tetris, and trial and error. (With emphasis on the error, and especially errors in reading comprehension. Note to self: don't start a puzzle when already tired. Or as someone might say: It's time to grab some "Z"s.)

I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch.

Well, at least I learned a lot about this puzzle type, and you get a Valentine's card as an answer for the main challenge.

The sixth and final Z (the one that appears separately from the initial burst) is the one on the top left. The rest should be more or less self-explanatory, so I didn't add any extra borders that might affect the artistic merit of the solution.

POST MORTEM/SCRIPTUM

I had misunderstood OP's piece order, but no worries, everything still works, and the heart shape only needs one easy tuck (piece number 5) that's definitely doable in Classic Tetris too.

(My apologies about the eye-sore. Why can't I re-spoilerize that picture..)

Method:

There are a couple of main constraints (as far as I noticed) in the puzzle:

1. Whenever you cut off an empty area, and don't have a plan to reconnect it (by making rows disappear), its size must be divisible by four.
2. The T piece's position is restricted by parity: if you imagine a checkerboard pattern on the background, then every piece except the T will contain 2 dark and 2 light squares. The greyed-out squares are correctly imbalanced to take the T piece into account, but half of the positions on the board would increase the imbalance, instead of bringing it back to zero.
3. the number of extra Zs must be divisible by 5: the number of extra squares they contain must be divisible by the line length. So 5 extra Zs is the absolute minimum.

Apart from those, it was mostly just playing Tetris, and trial and error. (With emphasis on the error, and especially errors in reading comprehension. Note to self: don't start a puzzle when already tired. Or as someone might say: It's time to grab some "Z"s.)

I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch.

Well, at least I learned a lot about this puzzle type, and you get a Valentine's card as an answer for the main challenge.

The sixth and final Z (the one that appears separately from the initial burst) is the one on the top left. The rest should be more or less self-explanatory, so I didn't add any extra borders that might affect the artistic merit of the solution.

POST MORTEM/SCRIPTUM

I had misunderstood OP's piece order, but no worries, everything still works, and the heart shape only needs one easy tuck (piece number 5) that's definitely doable in Classic Tetris too.

(My apologies about the eye-sore. Why can't I re-spoilerize that picture..)

Method:

There are two main constraint (as far as I noticed) in the puzzle:

1. Whenever you cut off an empty area, and don't have a plan to reconnect it (by making a row disappear), its size must be divisible by four.
2. The T piece's position is restricted by parity: if you imagine a checkerboard pattern on the background, then every piece except the T will contain 2 dark and 2 light squares. The greyed-out squares are correctly imbalanced to take the T piece into account, but half of the positions on the board would increase the imbalance, instead of bringing it back to zero.

Apart from those, it was mostly just playing Tetris, and trial and error. (With emphasis on the error, and especially errors in reading comprehension. Note to self: don't start a puzzle when already tired..)

I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch.

Well, at least I learned a lot about this puzzle type, and you get a Valentine's card as an answer for the main challenge.

The sixth and final Z (the one that appears separately from the initial burst) is the one on the top left. The rest should be more or less self-explanatory, so I didn't add any extra borders that might affect the artistic merit of the solution.

POST MORTEM/SCRIPTUM

I had misunderstood OP's piece order, but no worries, everything still works, and the heart shape only needs one easy tuck (piece number 5) that's definitely doable in Classic Tetris too.

(My apologies about the eye-sore. Why can't I re-spoilerize that picture..)

Method:

There are a couple of main constraints (as far as I noticed) in the puzzle:

1. Whenever you cut off an empty area, and don't have a plan to reconnect it (by making rows disappear), its size must be divisible by four.
2. The T piece's position is restricted by parity: if you imagine a checkerboard pattern on the background, then every piece except the T will contain 2 dark and 2 light squares. The greyed-out squares are correctly imbalanced to take the T piece into account, but half of the positions on the board would increase the imbalance, instead of bringing it back to zero.
3. the number of extra Zs must be divisible by 5: the number of extra squares they contain must be divisible by the line length. So 5 extra Zs is the absolute minimum.

Apart from those, it was mostly just playing Tetris, and trial and error. (With emphasis on the error, and especially errors in reading comprehension. Note to self: don't start a puzzle when already tired. Or as someone might say: It's time to grab some "Z"s.)

I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch.

Well, at least I learned a lot about this puzzle type, and you get a Valentine's card as an answer for the main challenge.

The sixth and final Z (the one that appears separately from the initial burst) is the one on the top left. The rest should be more or less self-explanatory, so I didn't add any extra borders that might affect the artistic merit of the solution.

POST MORTEM/SCRIPTUM

I had misunderstood OP's piece order, but no worries, everything still works, and the heart shape only needs one easy tuck (piece number 5) that's definitely doable in Classic Tetris too.

(My apologies about the eye-sore. Why can't I re-spoilerize that picture..)

I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch.

Well, at least I learned a lot about this puzzle type, and you get a Valentine's card as an answer for the main challenge.

The sixth and final Z (the one that appears separately from the initial burst) is the one on the top left. The rest should be more or less self-explanatory, so I didn't add any extra borders that might affect the artistic merit of the solution.

POST MORTEM/SCRIPTUM

I had misunderstood OP's piece order, but no worries, everything still works, and the heart shape only needs one easy tuck (piece number 5) that's definitely doable in Classic Tetris too.

(My apologies about the eye-sore. Why can't I re-spoilerize that picture..)

Method:

There are two main constraint (as far as I noticed) in the puzzle:

1. Whenever you cut off an empty area, and don't have a plan to reconnect it (by making a row disappear), its size must be divisible by four.
2. The T piece's position is restricted by parity: if you imagine a checkerboard pattern on the background, then every piece except the T will contain 2 dark and 2 light squares. The greyed-out squares are correctly imbalanced to take the T piece into account, but half of the positions on the board would increase the imbalance, instead of bringing it back to zero.

Apart from those, it was mostly just playing Tetris, and trial and error. (With emphasis on the error, and especially errors in reading comprehension. Note to self: don't start a puzzle when already tired..)