Using your Head is Permitted

October 2016 riddle

This month's riddle is an absolute classic (I don't even know its true origins), so no Internet searching please.

The question is this:
Can you tile a convex polygon with a finite number of concave quadrilaterals?

To be considered a solver, either give a proof of impossibility or construct an example tiling.

For completeness, a shape is called convex if for any two points in it, the entire straight line segment between them is also in it. Concave is the opposite. And by "tiling" we mean a partitioning of the area of the polygon.

List of solvers:

Joseph DeVincentis (3 October 00:15)
Kang Jin Cho (3 October 01:49)
Dan Dima (4 October 19:50)
Radu-Alexandru Todor (5 October 21:03)
Harald Bögeholz (7 October 00:03)
Zhu Haihui (13 October 23:09)
Luke Pebody (16 October 18:51)
Lin Jin (16 October 22:27)
Liu Yi (23 October 01:24)
Lorenz Reichel (30 October 00:09)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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