It is known that one can have 4 shapes in a plane all touching each other, and not 5. You can add requirements to the 4 shape problem:
- Can you do it with 4 equal triangles? (No)
- Can you do it with 4 equal rectangles? (No)
- Can you do it with 4 triangles with equal area? (Yes) (figure 1)
- Can you do it with 4 equal shapes? (Yes) (figure 2).
My question is: what is the simplest single shape which you can do it with?
(Figure 2 was easy to find, but it looks like it can be improved upon ;-).
(Simpler is undefined, but build from less than 11 squares would fit)
(I could not find a source to this problem. Is there?)