Suppose you had two stained-glass tiles in the shapes of polygons and you laid them on top of each other. Their overlapping area also forms a polygon, like the ones I have shown in the image: enter image description here

Notice how the blue squares overlap to form a triangle, the green triangles overlap to form a quadrilateral, and the orange polygons overlap to form two disjoint polygons: a triangle and a quadrilateral. Here is your challenge:

  1. Overlap a triangle and a square to form a septagon.
  2. Overlap a triangle and a quadrilateral to form an octagon.
  3. Overlap two quadrilaterals to form two disjoint polygons: one septagon, and one quadrilateral.
  4. Overlap two quadrilaterals to form a decagon.
  5. Overlap two hexagons to form a 16-gon.

Remember that the polygons need not always be convex!

  • $\begingroup$ Can I politely suggest that you don't post as many puzzles in such a short amount of time? They will get less attention and people prefer to look at one puzzle at a time $\endgroup$ May 21 '17 at 19:50
  • $\begingroup$ Fair enough. I was just going through all of my old notebooks and I found a bunch of old ones that I made. Should I delete some of them and save them for later? $\endgroup$ May 21 '17 at 19:51
  • $\begingroup$ Don't delete them now, but just hold back in the future. They still look like good puzzles, but I can't look at them all at once :) $\endgroup$ May 21 '17 at 19:54
  • $\begingroup$ Okay, sorry about that. $\endgroup$ May 21 '17 at 19:54
  • $\begingroup$ @Frpzzd I like them all, Thanks for sharing this pretty good question. need to sleep now, if noone solves the last one, I will do it :) $\endgroup$
    – Oray
    May 21 '17 at 21:43
  1. enter image description here

  2. enter image description here

  3. enter image description here

  4. enter image description here

  5. by Boboquack

enter image description here

Here are the solution for all shapes!

  • $\begingroup$ I've cleaned up 5 $\endgroup$
    – boboquack
    May 21 '17 at 23:28

And the answer to part 5 (sorry Oray):


With congruent polygons:

Another 16-gon

  • $\begingroup$ Wow... that looks really messy, but you did it! Good job! $\endgroup$ May 21 '17 at 22:23
  • $\begingroup$ @Frpzzd Cleaned up now $\endgroup$
    – boboquack
    May 21 '17 at 23:22
  • $\begingroup$ ... now can you do it with two congruent polygons? $\endgroup$ May 21 '17 at 23:23
  • $\begingroup$ @Frpzzd You should probably ask that as a separate question $\endgroup$
    – boboquack
    May 21 '17 at 23:24
  • $\begingroup$ Nah, it's not that hard... $\endgroup$ May 21 '17 at 23:49

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