Using some or all of the hexiamonds (pictured), make a star. You may flip pieces. The usual tiling rules apply, no overlaps, no gaps. Use only one or none of each piece. Answer is unique. Target shape also pictured, NB not to scale. Level of difficulty - nontrivial but not out of range for most is my guess.

The 12 hexiamonds Star dodeciamond

  • $\begingroup$ Are each of the small triangles equilateral? $\endgroup$ – ZanyG Jan 7 '20 at 4:18
  • $\begingroup$ @ZanyG yes all equilateral triangles $\endgroup$ – theonetruepath Jan 7 '20 at 5:53

Started by scaling the goal, I put one-by-one with some trial-and-error in the end to find this solution:

enter image description here

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    $\begingroup$ I find it oddly appropriate that you have a Tetris-themed avatar :) $\endgroup$ – Kos Jan 7 '20 at 22:16
  • $\begingroup$ So both solutions came up with a 2-length edged star, I'm curious if there could be a 3-length star - by my count there are exactly enough triangles to do it if you used every piece. Would take a lot more experimentation (or possibly programming) to come up with that one... $\endgroup$ – Darrel Hoffman Jan 8 '20 at 14:43
  • $\begingroup$ @DarrelHoffman The 3-length star has 108 cells to be covered, which means we need at least 18 pieces. Unfortunately, there are only 12 pieces. $\endgroup$ – athin Jan 8 '20 at 22:09
  • $\begingroup$ ...Oh, right. For some reason I was thinking each point would have 6 triangles, not 9, but I'm thinking about arranging circles in a triangle, not other triangles. Ignore me. $\endgroup$ – Darrel Hoffman Jan 9 '20 at 1:34

Having a Blokus Trigon set at hand was a big help!

I arrived at a different actually the same solution as pointed out:


My approach was rather straightforward, here's how I went around it:

Hint 1:

I was able to quickly rule out the little hexagon piece from the solution. This simplified things a lot. Once the hexagon is in the centre, there's big scarcity of pieces that can fill the corners, so that strategy seems doomed. (Other positions for the little hexagon are even worse.)

Hint 2:

I started my search with the next most awkward piece (the red "H shape", as I call it), placed it in a natural position, and then things kind of clicked from there with very little backtracking.

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    $\begingroup$ "looks like there's more than one after all" It is actually the same solution, just in mirror image. $\endgroup$ – Jaap Scherphuis Jan 7 '20 at 22:18
  • $\begingroup$ Well...the colors are different :) Two people so far that found it straight forward, but obviously we're only hearing from those people. I would like to know how many people tried it and found it difficult... $\endgroup$ – theonetruepath Jan 8 '20 at 1:31
  • $\begingroup$ @JaapScherphuis Oops you're right, I confused two pieces. $\endgroup$ – Kos Jan 19 '20 at 22:06

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