# Overlapping Tiles

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:

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!

• 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 Commented May 21, 2017 at 19:50
• 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? Commented May 21, 2017 at 19:51
• 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 :) Commented May 21, 2017 at 19:54
• Okay, sorry about that. Commented May 21, 2017 at 19:54
• @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 :)
– Oray
Commented May 21, 2017 at 21:43

1. by Boboquack

Here are the solution for all shapes!

• I've cleaned up 5 Commented May 21, 2017 at 23:28

And the answer to part 5 (sorry Oray):

With congruent polygons:

• Wow... that looks really messy, but you did it! Good job! Commented May 21, 2017 at 22:23
• @Frpzzd Cleaned up now Commented May 21, 2017 at 23:22
• ... now can you do it with two congruent polygons? Commented May 21, 2017 at 23:23
• @Frpzzd You should probably ask that as a separate question Commented May 21, 2017 at 23:24
• Nah, it's not that hard... Commented May 21, 2017 at 23:49