Original Math Notes
All Seasons
Season 5
Episode 523: Angels and Devils
Generation of an infinite chess board
Scene 38:
          No... it's a puzzle.

And he assembles the pieces --

                  LARRY (cont'd)
          Six piece puzzles dating from the
          1800s... traditionally, notched wood
          that assembles into the form of a
          seed burr --

-- into a remarkably snug-fitting BURR PUZZLE --

          Bill Cutler proved that there are 25
          possible notchable pieces to make
          solid six-piece burrs -- and they can
          be assembled 314 ways...

          Great -- he's not a psycho, he's a
          puzzle fan --

3D Dissection Puzzle »

This 3D dissection puzzle requires sequential assembling of its parts. The red, green and blue solids are rotated instances of the same shape. They have to be assembled first before the two rotated versions of the second shape shown in cyan and magenta can be attached. The gray shape is the corner stone which completes the puzzle. Rotate the cube to see the puzzle and its pieces from different angles.
Scene 38:
          He's all about symbols -- metaphors --

Don turns to the plasma -- starts FAST FORWARDING through the
Duryea interview --

          A Burr has a key piece -- if you pull
          it out --

LARRY pulls one piece -- and the PUZZLE COLLAPSES AGAIN.

                  LARRY (cont'd)
          -- everything falls apart.

Touching Planar Polycubes »

A planar polycube is a polycube that can be placed in such a way that it extends only one cube high into the third dimension. For each known integer n, here are the smallest known planar polycubes such that n congruent copies all touch each other. This problem area is far from fully analyzed or understood and you might well find better solutions than the ones presented here.
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