Are You a Math Genius?
As mentioned in the episode, Bill Cutler analyzed the classic solid burr puzzle in 1978. Other compilations are given in The Puzzling World of Polyhedral Dissections by Stewart Coffin. Burr puzzles with interior holes allow for more complex solutions with one example being Bill's Baffling Burr, which requires 5 moves for the first piece to be removed. An extreme example in simple 6-piece burrs is Gordian's Knot by Frans de Vreudg, which requires 28 moves to remove one piece. A variety of different burrs are compiled at the site Puzzle will be played by Ishino Keiichiro. Many of these puzzles can be solved and analyzed by the free program Burr Tools.
Solid Burr
Wolfram SpikeyPuzzles provided by Wolfram Research, Makers of Mathematica