Blue Ox (Solution)

by Eli Bogart and David Farhi

Here is an unordered list of answers to the twenty round puzzles, for reference. The colors identify which puzzle answer this is (e.g. DAMP is the answer to the red/green edge cubelet).
        RYB   SHLEP
        RY    EXTANT
        RYG   DEDITION
        RG    DAMP
        RWG   BOIL
        RW    UNARY
        RWB   CONTIGUOUS
        RB    BASSIST
        YB    SLAUGHTER
        YG    BEER CHUGGING
        WG    EDITH PIAF
        WB    CREAM OF TARTAR
        OYB   ARMORED RECON
        OY    HYPAPANTE
        OYG   COMMEMORATIVE BATS
        OG    DERRICK TRUCK
        OWG   BROWN ROT
        OW    ATTORNEYS GENERAL
        OWB   SACROSANCT
        OB    IMPROMPTU
    

Each face is a different shade of blue. Their hex codes (clued by the title, and visible by looking at the source for the page) are:

  2001FF 3A00FF 2020FF
  0041FF 3A45FF 0420FF
  2A20FF 2401FF 3005FF

Each non-blue digit takes only 3 values over the whole grid: 0 and two others. So we turn it into four 3x3 grids:

1st digit

  232
  030
  223

2nd digit

  0A0
  0A4
  A40

3rd digit

  002
  442
  200

4th digit

  100
  150
  015

Each of these four looks like a tic-tac-toe grid. In each case there is a unique completion of the game assuming optimal play. For example, for the second digit it must be player 4s turn (he has played fewer times). 4 plays in the upper right, then A plays in the lower left, then 4 in the upper right, then A in the middle right. This gives us a string of 4 letters: the 4th letter of the upper right answer, then the Ath (10th) letter of the lower right, then the 4th letter of the upper left, then the Ath of the middle. Those are ECTR.

In this manner the games of tic-tac-toe give:

EL
ECTR
OOSM
OSIS

spelling out the answer, ELECTROOSMOSIS.