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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.
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    $\begingroup$ @Alderath No background color is allowed per the last bullet point. $\endgroup$
    – noedne
    Commented Feb 28, 2022 at 10:01
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    $\begingroup$ 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. $\endgroup$
    – Robin Clower
    Commented Feb 28, 2022 at 15:05
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    $\begingroup$ @RobinClower "In her version of the game, the pieces use the standard colors and can drop in any possible order without restrictions." $\endgroup$
    – samm82
    Commented Feb 28, 2022 at 16:50
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    $\begingroup$ Ah, I was looking for that in the clarifications section :facepalm: $\endgroup$
    – Robin Clower
    Commented Feb 28, 2022 at 19:02
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    $\begingroup$ @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. $\endgroup$
    – noedne
    Commented Mar 1, 2022 at 21:55

1 Answer 1

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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.

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    $\begingroup$ @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? $\endgroup$
    – BruceWayne
    Commented Feb 28, 2022 at 2:19
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    $\begingroup$ @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 :) $\endgroup$
    – noedne
    Commented Feb 28, 2022 at 2:59
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    $\begingroup$ @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. $\endgroup$
    – noedne
    Commented Feb 28, 2022 at 3:05
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    $\begingroup$ If you don't mind a pixelated version, Palau might be possible... $\endgroup$
    – Darrel Hoffman
    Commented Feb 28, 2022 at 14:57
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    $\begingroup$ @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. $\endgroup$
    – ilkkachu
    Commented Mar 1, 2022 at 23:34

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