Let the balls in the bag be represented by the 3-tuple (r,w,b);
where r, w, and b are the number of red, white, and blue balls
mod 3. The starting position is (0,1,2), the required ending
position is 0,0,0), and for the procedure -
(n-1)mod 3 = (n+2)mod 3.
(0,1,2) -->
(2,0,1) -->
(1,2,0) -->
(0,1,2) -->
repeat
Can never reach position (0,0,0).
QED
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