Why the 14-15 puzzle is impossible, and how to solve it anyway

From a channel Lumen includes in full: Henry Segerman, a mathematician and artist, explains geometry and topology through 3D-printed models and physical objects (hyperbolic space, 4D shapes, knots).

A 6-minute video from Henry Segerman's catalogue; the title names its topic.

Video by Henry Segerman, played through YouTube's embedded player.