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I was staring at my window last night, and daydreaming (nightdreaming?) about filling it with shapes. Suddenly, I was struck with inspiration for a new type of puzzle! Here's a fairly easy instance:

polyominoes 1

Pack the colored polyominoes into the white area, without rotating them, so that they fill it perfectly.

What's that? The green piece can't fit, you say? Oh right, I forgot to mention: The gray walls are portals. Any piece that would normally overlap a gray wall goes through it entirely, as if there were no space there at all. The gray border around the puzzle loops, as well - pieces that would stick off the right side of the board reappear at the left, and so on.


To demonstrate, here's an example packing:

polyominoes 2

Notice how the blue block warps from C1 to C3, across the wall at C2.

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    $\begingroup$ What happens if the center of the green piece overlaps the middle portal? $\endgroup$ – Matthew Wells Jan 26 at 10:05
  • $\begingroup$ This is very cool! $\endgroup$ – Dmitry Kamenetsky Jan 26 at 10:24
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    $\begingroup$ @MatthewWells The piece simply won't fit. Each edge of the wall acts as a teleporter to the opposite side, but the actual interior of the wall is just solid. $\endgroup$ – Woofmao Jan 26 at 15:40
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    $\begingroup$ As an aside, the best implementation of pentomino puzzles I've seen is in an old (but still living!) game called Puzzle Pirates. The "Carpentry" duty station which was used to keep your ship from falling apart was pure pentomino fun where you'd have to fit one of three given shapes into one of four puzzles without neglecting any of them for too long. Extra points for clearing a puzzle with the same tiled piece or by keeping the "Grain" of a patch job the same (never rotating a piece only 90 degrees) $\endgroup$ – Adam Smith Jan 27 at 6:47
  • $\begingroup$ For any future puzzles: theres a bit of confusion about the answer, and how the portal works. In the answer, the whole of the left side of the red gets transported, suggesting that the portal teleports all connected cells (you can kinda see this with the white outline in the example. I'd recommend clarifying this so people don't get confused. Great puzzle though! $\endgroup$ – Beastly Gerbil Jan 27 at 13:33
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This works! (I think)

enter image description here

(Hopefully that’s clear enough how the shapes go)

I got this mostly by thinking about how the blue and red can be placed such that the top and bottom of the green can be transported up and down without overlapping.

Brilliant idea! Hope to see some more!

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    $\begingroup$ How can B3 or E3 phase through without a portal along row 3? $\endgroup$ – personjerry Jan 26 at 15:30
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    $\begingroup$ @personjerry the portal splits the red shape into 2. The whole left side of the red shifts to the left, not just one cell $\endgroup$ – Beastly Gerbil Jan 26 at 15:31
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    $\begingroup$ I agree that's the only way it's solvable, but that's not consistent with the puzzle description. Only pieces that overlap grey areas wrap, it says nothing about attached blocks moving $\endgroup$ – Mohirl Jan 27 at 13:06
  • $\begingroup$ @Mohirl true, it could probably be clarified in the question. As you say, this is the only solution so it must be true, just needs to be made clear from the start $\endgroup$ – Beastly Gerbil Jan 27 at 13:17
  • $\begingroup$ I'm at a complete loss for what is and isn't allowed in the middle grey box given the comments on OP and this accepted solve. Why is red allowed to interact this way, but green couldn't be placed one row lower? (Not by the logic to solve, but by the rules of the puzzle) $\endgroup$ – TCooper Jan 27 at 18:18
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I think the answer is

B G G G B
B R . R R
B R G G R

Thought process:

I figured that the three pieces cannot make up the required number of cells for each column, at least without a piece going through the center gray cell horizontally. There are five ways to horizontally go through the center gray cell, so I tried one by one until the column sum became feasible.

And indeed it's an interesting kind of a puzzle I've never seen before. Nice job.

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