deutsche Version

Jigsaw puzzle with four parts

My learned colleague Professor Götz directed my attention to the following problem. The four coloured areas are moved, their shape remains exactly the same ... but look what happens:

Solution

Both polygones are not triangles but (different) quadrilaterals. Figure 1 shows (in an exaggerated way) the deviation of these quadrilaterals from a triangle. The lower quadrilateral is convex, the upper one is not.


Figure 1

Figure 2 shows the exact representation of both near-triangular quadrilaterals. As all vertices of both quadrilaterals coincide with a lattice point (see the grey crosses) their areas are easily calculated to 32 and 33 square units.


Figure 2