Episode 8: You are in the mood to tile your bathroom with pentagonal tiles? Sure, why not, but how do you do it? The question may seem silly, but has actually haunted mathematicians for over a century. Tiling a plane with convex pentagons without leaving any hole is indeed far from being easy. Since 1918, up to 15 types of pentagons able to do that have gradually been discovered. But how many more exist? In 2017, computer engineer Michaël Rao finally settled the issue. Using a special software program, he reduced the number of eligible pentagons from infinite to 371. A second software program helped select them to eventually find the correct number of pentagons able to tile a plane: 15, namely all those already discovered!