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I love designing perfect clear puzzles for my dear friend who loves Tetris. Here's a lovely puzzle I crafted today.

Original Puzzle (Warm-Up)

Starting with this field,
top row has columns 3, 4, and 8 filled; bottom row has all columns except 6 filled
place this exact sequence of pieces: O, S, L, I, Z, T, and J,
O piece S piece L piece I piece Z piece T piece J piece
where rotation is allowed but holding is not, so that the field is empty at the end.

The Challenge

After creating this puzzle, I remembered that my friend loves to "ZZZ...", so I would love to show them how much I care by adding extra copies of the (red) Z piece to the sequence, immediately after the first Z piece. Can you help me by finding the least number of Z pieces I need to add so that the puzzle can still be solved?

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  • $\begingroup$ dedicated to a friend <3 $\endgroup$
    – noedne
    Commented Feb 14, 2022 at 17:48
  • $\begingroup$ Do we fill the grey or black tiles? $\endgroup$
    – Nautilus
    Commented Feb 14, 2022 at 18:29
  • $\begingroup$ @Nautilus Black tiles are empty space. The grey tiles are the leftover minos from previously placed pieces. $\endgroup$
    – noedne
    Commented Feb 14, 2022 at 18:38
  • $\begingroup$ @Nautilus Yes, standard length of 10. The exact sequence should be followed, hence why holding a piece is not allowed. $\endgroup$
    – noedne
    Commented Feb 14, 2022 at 19:13
  • $\begingroup$ Does that mean the pieces should be treated as falling from above the rectangle? Let's say I block out a part of the rectangle with a piece, but that empty part is shaped like another piece. Can I still fill it with the latter? $\endgroup$
    – Nautilus
    Commented Feb 14, 2022 at 19:27

2 Answers 2

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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.

enter image description here

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.

enter image description here

(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.)

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  • $\begingroup$ What do you mean by "the initial burst"? Sorry if I was unclear, but the extra Z pieces appear immediately after the first Z piece, i.e., they are all consecutive ("ZZZ..."). $\endgroup$
    – noedne
    Commented Feb 15, 2022 at 2:29
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    $\begingroup$ Hmm, somehow I read that as "5 extra Zs that appear after the first piece in the sequence." In any case, a couple of tucks should be enough to make this shape in the intended order of pieces too. $\endgroup$
    – Bass
    Commented Feb 15, 2022 at 2:31
  • $\begingroup$ Apologies, I've edited the question to avoid misguiding future solvers. Could you please double check to make sure this still works with the intended sequence? $\endgroup$
    – noedne
    Commented Feb 15, 2022 at 2:41
  • $\begingroup$ Thank you for your perseverance! I hope my friend appreciates your lovely construction. $\endgroup$
    – noedne
    Commented Feb 15, 2022 at 2:54
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Warmup:

From the warmest color to the coolest: enter image description here

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    $\begingroup$ How did I not find this in 3 hours.. oh, I had copied the starting position wrong. Ouch. $\endgroup$
    – Bass
    Commented Feb 15, 2022 at 1:33
  • $\begingroup$ You can't put the J in after the T and I, which means you're holding pieces, which is not allowed in the question. $\endgroup$
    – trent
    Commented Feb 16, 2022 at 12:48
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    $\begingroup$ @trent You need to treat this puzzle as a real game of Tetris. $\endgroup$
    – Nautilus
    Commented Feb 16, 2022 at 14:46
  • $\begingroup$ What version of Tetris will allow you to place the J (purple) piece after T (dark blue) and I (green) have already been placed? Per the question, J is the last piece in the sequence, and holding is not allowed. $\endgroup$
    – trent
    Commented Feb 16, 2022 at 15:34
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    $\begingroup$ @trent After placing the T, the top line gets completed and cleared, allowing the J to be placed :) $\endgroup$
    – noedne
    Commented Feb 16, 2022 at 15:40

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