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Here's another set of polyominoes (sizes 4,5,6,7,8,9,10) that you can print and cut out. As before, the two smallest (same pieces as previous version) make a 3x3. The rest of the pieces are different. Also as before, add a piece at a time to make a 3x5, 11x2, 5x6, 3x13 and 7x7.

There's only one way to make each rectangle. You are allowed to flip pieces over.

If I feel energetic I might extend this by adding an 11-omino (6x10) and 12-omino (8*9).

The reason the first two are the same... those are the only two that work.

Polyominoes size 4 through 10

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  • $\begingroup$ Did you create a script to generate those problems? I like those ! $\endgroup$
    – Florian Bourse
    Commented Jan 5, 2018 at 12:43
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    $\begingroup$ @prog_SAHIL (probably) recommends that you use craftdesignonline.com/pattern-grid instead of actually printing the pieces. You can find instructions for creating "pretty" solution images with Gimp at the bottom of my answer to the previous puzzle. $\endgroup$
    – Bass
    Commented Jan 5, 2018 at 12:46
  • $\begingroup$ I have a program that tiles with polyominoes. I ran it with all sizes of polyomino from 1 through 10. Initially I solved the 3x3 with just sizes 4 and 5, then eliminated all non-unique tilings, saving the list of pieces that tiled. I then augmented the successful list with each of the hexominos and tiled the 3x5, then augmented again etc. Last step took about a week and found about 73000 sets of pieces. I have a Render program to draw the pieces. $\endgroup$
    – theonetruepath
    Commented Jan 5, 2018 at 12:53

1 Answer 1

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This seems to work:

3x3

enter image description here

5x3

enter image description here

11x2

enter image description here

5x6

enter image description here

13x3

enter image description here

7x7

enter image description here

All in one picture

enter image description here

I made the pictures with excel. Manually selecting the cells in the correct shape and colouring might not be the most efficient way for trial and error, but it creates pretty good pictures.

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  • $\begingroup$ You just beat me to it . Damn! Great bro. $\endgroup$
    – prog_SAHIL
    Commented Jan 5, 2018 at 13:18
  • $\begingroup$ @prog_SAHIL Yeah, every minute I was working on it I got more afraid that someone would beat me to it. Luckily that didn't happen (for me at least - not for the others :P) $\endgroup$
    – Lolgast
    Commented Jan 5, 2018 at 13:25
  • $\begingroup$ Well done! For the benefit of future solvers (not spoiling the other answers if they want to peek at one), it would be better to split each solution to its own spoiler tag. I can do the edit if it’s ok with you. $\endgroup$
    – Bass
    Commented Jan 5, 2018 at 14:04
  • $\begingroup$ @Bass fine with me. Haven't got the time myself right now, so if you want to do it, go ahead :) $\endgroup$
    – Lolgast
    Commented Jan 5, 2018 at 14:08
  • $\begingroup$ @Bass Thanks! [insert characters for minimum amount] $\endgroup$
    – Lolgast
    Commented Jan 5, 2018 at 14:51

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