Symmetrical solutions with 5 tetratans



This project was initiated by Tick Wang, a puzzle enthusiast from Shanghai, in January 2022, as an addendum to our Tan Tricks sets. If you already own the set, use the pieces shown and have fun solving. Even if you don't own the set, you can just make cardboard cutouts of these five shapes.

Tick examined the 14 tetratans and set aside all the pieces that were convex or symmetrical. He was left with these five rather irregular tiles:

Tick's goal was to find all the symmetrical shapes that could be formed by 2, 3, 4, and all 5 of these tetratans. He noticed that certain two pieces always occurred, in every shape, and the question is: Can any 3- or 4-piece symmetrical shape be formed without including both of those pieces? Can you find a proof either way? The first solver to send us such a proof will win a prize. Our email address: Kadon Enterprises, Inc.

Here are a few sample solutions using 2, 3, 4, and all 5 pieces. Do you detect which two pieces are always present? Piece colors are shown as different for artistic effect only, to highlight each piece.


The full collection
Here is the entire collection of the 160 symmetrical shapes derived by George Sicherman that can be solved with Tick's quaint quintet. It is interesting to find that there are three kinds of symmetry:

  • Orthogonal (mirror symmetry vertical on the grid): 38
  • Diagonal (tilted by 45 degrees on the grid): 64
  • Rotational (turned halfway, like the letters S and Z): 58

    Further, there are 55 figures with holes enclosed, anywhere from a single triangle to 6 triangles.

    Have fun solving these. Also see how many 3-piece and 4-piece symmetries you can find.


    Now to improvise artistic shapes...
    Another way to play with this handful of tricky pieces is to invent and build funny figures. Tick Wang is famous for his imaginative free-form characters. Here are a couple of cute shapes by Kate to amuse him: a goose and a puppy.




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