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Quiz of the Month (February 2002)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

     1.  2
     2.  6
     3.  6
     4.  (Bonus Question)  14
Notes
The following are the only distinct solutions. Any other apparent solution either has adjacent sectors the same colour, or is a cyclical permutation of another solution, and so is indistinguishable from it.
  1.        R G B
            R B G

  2.        G R G R        B R B R
            B R G R        B G B R
            G B G R        B G B G

  3.        B G R G R      B G B G R
            G B R G R      G B R B R
            B R B G R      G B G B R

  4.(Bonus) G R G R G R    B G R B G R    B G B R B R
            B R G R G R    G B R B G R    G B R G B R
            G B G R G R    B R G B G R    B G B G B R
            B R B R G R    G B G B G R    B G B G B G
            B G B R G R    B R B R B R

THIS MONTH'S QUIZ

   1. The manufacturer of another board-game, not to be outdone
       by last month's game, uses for counters a number of
       wooden cubes, all the same size. Each cube has three faces
       painted red and three green. How many distinguishable cubes
       can there be? 
       
   2. Another game uses a similar set of cubes, with each face
       painted red or green without restriction. How many
       distinguishable cubes can there be in this game?

   3. Yet another game uses similar cubes, and each has two red
       faces, two green faces and two blue faces. How many
       distinguishable cubes can there be in this case?

***

(c) Hector C. Parr (2002)


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