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 Red, White, and Blue (Posted on 2015-07-29)

A bag contains 3 red, 4 white, and 5 blue balls. Two balls of different
color are removed from the bag and replaced with two balls of the third color.

Prove that no matter how many times this procedure is repeated, it is impossible for all twelve balls in the bag to be the same color.

 Submitted by Bractals Rating: 4.0000 (1 votes) Solution: (Hide) 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

 Subject Author Date re: Yet another approach... @Paul & Bractals Ady TZIDON 2015-07-30 01:59:48 Yet another approach. Jer 2015-07-29 18:56:37 proof Paul 2015-07-29 15:47:02 computer proof Charlie 2015-07-29 14:35:28

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