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An archaeological artifact is depicting figures of some natural and artificial objects like the sun, moon, comet, star, flower, horse, bird , insect, headdress, mountains, river, house, weapons, bonfire and necklace. The translation of the symbol message below is "WIND, RAIN, FLAME, SOIL, ESSENCE". According to experts, there are 5 polyomino tiles that were used as patterns for making the outline of the figures in this artwork. They also believed that these 5 tiles altogether should fill and fit in any of the 16 figures depicted above. What are these polyominoes?

Note: one figure in original puzzle image was replaced due to wrong drawing of the bonfire. An acceptable solution nevertheless was provided by Lucas Rotter. Thanks to his effort for we could have not known it. But edition was necessary for it was stated in the OP that the 5 tiles pattern applies to figures in artwork. The frog, perfume bottle and the hanukkah also got edits while more objects were added.

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    $\begingroup$ This is tough! At least with trial and error. I've got some configuraions, but they always fail for one of the shapes. By the way, what's your stance on flipped polyominoes? Usually polyominoes can be rotated, but not flipped. For example the S/Z and J/L pentominoes are distinct. Is flipping allowed? $\endgroup$
    – M Oehm
    Nov 25, 2016 at 21:38
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    $\begingroup$ Flipping makes more symmetry and allowed naturally $\endgroup$
    – TSLF
    Nov 26, 2016 at 3:28
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    $\begingroup$ Can we assume that all the straight lines are integer lengths? $\endgroup$
    – Dr Xorile
    Nov 26, 2016 at 23:08
  • $\begingroup$ yes every figure has 16 unit squares $\endgroup$
    – TSLF
    Nov 27, 2016 at 8:54

2 Answers 2

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All 16 shapes on the artefact can be made from ...

  • a domino (pink),
  • an I-tromino (purple),
  • an L-tromino (green),
  • an S-tetromino (light blue) and
  • an L-tetromino (ochre)


shapes on the artefact

All the shapes on the border of the artefact can be made from these polyominoes, too. (The assumption that this is true is useful, because it discounts all T-polyominoes and blocks that contain a 2×2 square.)

shapes on the border

Finally, the symbols at the bottom can be made from the five base polyominoes:

shapes in the symbolic language

The assumption that these symbols can be formed from the wanted polyominoes is useful, too. Two shapes – the bull's head (top right) and the two-armed candlestick (rightmost in the second row from the bottom) – each have a base of 6 units that is not aligned to the unit grid. That means we need two polyominoes that can form these two bases only, because the must be separate from the rest of the shape. I first had two L-shaped trominoes, but it turns out that three different polyominoes are used.

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This answer was posted when the puzzle looked like this. After the update of the image, this answer is incorrect. The current correct answer is M Oehm's.

If

WIND, RAIN, FLAME, SOIL, ESSENCE equals
enter image description here

then it's perfectly possible (OP confirmed that flipping is allowed). The monomino is the part that seems like utter cheating to me, but according to Wikipedia it's considered a polyomino.

Click to enlarge:
enter image description here.

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  • $\begingroup$ @ Lucas Rotter: accepted solution..but since the bonfire in the OP is wrongly outlined and needed to be edited (my sincere apologies), Let's see if there can be other to come up with the solution. The 5 polyomino solution actually solve every figure in the artwork. Can you give it another go? Hint: no square piece. $\endgroup$
    – TSLF
    Nov 27, 2016 at 6:58
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    $\begingroup$ @TSLF: Could you please make clear in the question that the pattern has been corrected? The bonfire (or headdress? the nomenclature isn't quite clear, since you üprovide 15 names for 16 shapes) was a major roadblock before and is even more so now with its two 3×1 stalks. $\endgroup$
    – M Oehm
    Nov 27, 2016 at 10:23
  • $\begingroup$ @TSLF Please also remove the checkmark from this answer, since it isn't correct anymore. $\endgroup$
    – user14478
    Nov 27, 2016 at 10:59

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