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Here are two figures, each composed of 54 pixels. Cut each figure into six nonominoes having the same shape and size.

  • Both figures use the same nonomino
  • The nonominoes could be rotated, reflected, or both
  • The four colors (blue, green, pink, gray) are for artistic effect only. These colors have no relationship to the solution.

Pixel-heads

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    $\begingroup$ Those nonominoes puzzles are great! Love them. $\endgroup$ – BmyGuest Jan 10 '15 at 11:11
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Found it!

enter image description here

Very nice! I wasted 30min until I've realized I mis-drew my black & white copy with only 53 squares! :c)


Edit: As requested, and for the purpose of this site (teaching how to build/solve puzzles) I'm adding how I found the solution to this puzzle.
General considerations:

  • Mostly by trial & error. I'm using a graphic program with layers/objects (i.e. Powerpoint) such that I can easily modify & clone tiles while trying fitting together the puzzle.
  • The tile-size of the nonominoes is known if all are of same size, the total field size is known, and the number of nomoninoes is known.
  • Then I start with one (in this case close to a hole) and copy/tilt it to see if they fit. Rule-out conditions are:
    • two noominoes overlap
    • isolated 'holes' are created
  • From there, it's a process of reduction, guided by intuition. (i.e. usually good puzzles have rather 'complicated' nonomino-shapes. So I try those first.)
  • Sometimes it helps to do the process with a partial nonomino (i.e. of smaller size) first. This rules out whole sets of shapes. (If you have a problem with a 5-sized shape, no bigger shape will work out.)

As for this particular puzzle:

- The tile-size of the nonominoes is known to be 9, because we have to fit 6 tiles into 54 fields, hence: 6 x 9 = 54.
In the particular puzzle, it was soon clear that nonominoes had to partly wrap around a one-square hole. Few tries showed that it had to be a "5-tiles around hole" solution.
- So I made this 5-sized nonomino and copied it 6 times, arranging it around the head-holes.
- Then I successively added 1 square (i.e. made all 6-sized, 7-sized...). One could immediately see, what fits, and what wouldn't. As always: You must not create overlaps and you must not create isolated holes. - I actually only solved the left head. It was then immediately visible, that the right one has just a mirror in it's left half.

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    $\begingroup$ Is there any special way to solve things like this? I had no idea how to even start thinking. $\endgroup$ – Quark Jan 10 '15 at 22:15
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    $\begingroup$ @Quark: I've edited in some guidelines and my path to the solution. Thanks for suggesting it. This site is about teaching, so such an edit is a very good idea indeed. $\endgroup$ – BmyGuest Jan 11 '15 at 10:38

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