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Weights and balls (Posted on 2013-01-09) Difficulty: 2 of 5
You are given 6 identical balls of same size and shape two of which are red. two white and two blue. It is known that one ball of each colour weighs 15 gm; while the other weighs 16 gm. Using a two-pan balance only twice how will you separate the balls of 16 gm weight?

No Solution Yet Submitted by Philip7086    
Rating: 4.0000 (1 votes)

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Solution solution | Comment 1 of 4

Call the balls R1, R2, W1, W2, B1, B2.

First weighing:   R1 & W1    vs    B1 & W2

If:                    R1+W1 = B1+W2

Weigh:                    R1 vs B1
        R1 < B1           R1  = B1           R1 > B1
        -------           --------           -------
         W1>W2           impossible           W1<W2
         R1<R2                                R1>R2
         B1>B2                                B1<B2


        
If:                    R1+W1 < B1+W2

Weigh                     R1 vs B2
        R1 < B2           R1  = B2           R1 > B2
        -------           --------           -------
         W1<W2             W1<W2              W1<W2
         R1<R2             R1<R2              R1>R2
         B1<B2             B1>B2              B1>B2


        
If:                    R1+W1 > B1+W2

Weigh                     R1 vs B2
        R1 < B2           R1  = B2           R1 > B2
        -------           --------           -------
         W1>W2             W1>W2              W1>W2
         R1<R2             R1>R2              R1>R2
         B1<B2             B1>B2              B1<B2        

  Posted by Charlie on 2013-01-09 18:11:00
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