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?

This problem is mainly about avoiding too much information.

To start with, set one white ball and one blue aside; they will never be needed.

(1)Weigh red+white-vs-red+blue.

(1a) If both sides are the same, the white and blue are unequal, so simply

(2a)switch the white and blue balls. The heavy side now contains 2 heavy balls, and the light side two lights, resolving all values.

(1b) Conversely, if there is an imbalance, the heavier side contains the heavier red, so we know which red is which, and can now

(2b) weigh both reds against the blue and white. Since the red side is neutral, if the blue+white side is lighter or heavier, then both balls are correspondingly lighter or heavier. If the two sides now balance, the ball with the heavy red before must also have been heavy, and the one with the lighter red before must also have been light, again resolving all values.

 

 

Edited on January 10, 2013, 8:53 am

Posted by broll on 2013-01-10 01:25:02