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Your friend is playing Tetris. In her version of the game, the pieces use the standard colors and can drop in any possible order without restrictions. In the order shown below, the colors are light blue, dark blue, orange, yellow, green, purple, and red.

the seven Tetris pieces: cyan I piece, blue J piece, orange L piece, yellow O piece, green S piece, purple T piece, and red Z piece

"Yes, I finally did it!" she exclaims. You worriedly glance over, afraid that she's finally beaten your high score. Much to your surprise, her score is still 0—she hasn't even cleared a line yet!

"What's the big deal?" you wonder aloud.

"I made my country's flag!" she cries triumphantly.

As you stare at the matrix of colored squares, your jaw drops in awe. Despite not having cleared a single line, she's managed to recreate her nation's flag!

Which countries could your friend be from?

Clarifications

  • No rows have been filled, and no lines have been cleared.
  • The playing field has ten columns.
  • The flag is a country's current official one (see Wikipedia for a good list).
  • All parts of the flag exactly match the shape and dimensions of their official design.
  • The flag is entirely colored using similarly colored pieces, without any empty space.
noedne
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  • It's a bit unclear what colour the background is. If there is no tetris piece occupying a space, is that space considered to be black or white? I have seen tetris games with both white or black backgrounds. – Alderath Feb 28 '22 at 09:59
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    @Alderath No background color is allowed per the last bullet point. – noedne Feb 28 '22 at 10:01
  • That first one looks more like cyan than light blue. And I think your "purple" one is actually magenta. – Toby Speight Feb 28 '22 at 14:24
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    I know too much about tetris to solve this. Modern tetris uses a "bag" system in which each separate piece will fall before a repeated piece falls, so there's actually no solution with the current restrictions. – Robin Clower Feb 28 '22 at 15:05
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    @RobinClower "In her version of the game, the pieces use the standard colors and can drop in any possible order without restrictions." – samm82 Feb 28 '22 at 16:50
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    Ah, I was looking for that in the clarifications section :facepalm: – Robin Clower Feb 28 '22 at 19:02
  • Must the country be a recognized country? If not, the flag of the micronation of Atlantium might also be possible. – bta Mar 01 '22 at 21:37
  • @bta It has a similar issue to rot13(Fjrqra): because of its aspect ratio (6:9) and the fact that a stack of O-tetrominoes can never be an odd height, it would have to be 12 tiles wide by 18 tiles high, violating constraint 2 – samm82 Mar 01 '22 at 21:52
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    @bta Good call out, she is from a recognized country, although I did not clarify this. If she were from an unrecognized country, then this would be totally open-ended. – noedne Mar 01 '22 at 21:55

1 Answers1

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The friend is from Ukraine, as their flag (rotated 90 degrees in either direction) can be formed on the grid, preserving the 2:3 ratio of the flag (and the equally-sized stripes). This is the only flag that works, since based on the constraints of the puzzle, the flag must only consist of areas with square borders (ie. no symbols, circles, triangles, stars, etc.) and cannot contain white or black, which greatly reduces the number of valid flags. Additionally, since (I'm pretty sure) it is impossible to form a rectangular region with the S- and Z-tetrominoes, the flag must be made of blue, orange, yellow, and/or purple polygons with sides connected at right angles, leaving only Sweden and Ukraine to fit this description. Sweden's flag is an invalid option, as to "exactly match [its] dimensions", the flag (rotated 90 degrees in either direction) would have to be ten tiles wide, violating the first constraint (the "thicknesses" of each colour in the Swedish flag horizontally are 5, 2, and 9, respectively, which can't be scaled down to integer values).

Ukraine's flag made with tetrominoes

I don't know if this is appropriate for this site, but consider donating to organizations that support those in Ukraine right now, like Save the Children.

samm82
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  • Are there any other such countries? – Greg Martin Feb 27 '22 at 07:12
  • @GregMartin I've added an explanation for why I think this is the only one – samm82 Feb 27 '22 at 16:09
  • The puzzle says "countries" meaning that there are multiple answers – Some Guy Feb 28 '22 at 00:54
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    @SomeGuy does that necessarily mean OP knows of other solutions? It's possible they're just asking and used plural because they assumed at least two could be found? – BruceWayne Feb 28 '22 at 02:19
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    @samm82 Nice job finding Sweden! It was really the only viable alternative, and I very narrowly ruled it out with my specific choice of rules (sorry, Sweden). Thanks for the great answer and for helping raise awareness! Let's help our friend :) – noedne Feb 28 '22 at 02:59
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    @BruceWayne I made sure that the answer is unique, but I chose to use the plural to avoid giving this away and to encourage the solver to discover this as well. – noedne Feb 28 '22 at 03:05
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    If you don't mind a pixelated version, Palau might be possible... – Darrel Hoffman Feb 28 '22 at 14:57
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    @samm82, argh, yes. Yes, of course you're right, scaling in integer sizes is the obvious first issue for scaling down. Well, would have been, if I wasn't a fool. Sorry. Fun fact: all the nordic cross flags have different proportions. And kind of convenient for the sake of this question that the flag of the correct answer does have such nice proportions. – ilkkachu Mar 01 '22 at 23:34
  • @ilkkachu No worries! – samm82 Mar 01 '22 at 23:39