20 Oct, 2010

10 cricket balls one is heavier or lighter. Find the ball in 3 weighing chances.

Lets name the balls 0 1 2 3 4 5 6 7 8 9 for convinience. Step 1 : Take 3 balls from this set lets take 0 1 2 and weigh it against 3 4 5. Weighing 1. Step 1.1 : Now suppose both of them are of different weight. It means 6 7 8 9 are all of identical weight and can be used as a reference. Step 1.1.1 : Take the lighter of the set, lets suppose it is 0 1 2 Step 1.1.2 : Weigh 0 1 2 against 6 7 8 (Reference). Weigh 2 Step 1.1.2.1: Suppose 0 1 2 and 6 7 8 stay balanced, we infer that the set 3 4 5 has a heavier Ball. else, we can infer that 0 1 2 has a lighter ball. Step 1.1.2.1.1 : Now given a set of 3 you can weigh any 2 and find the odd one out since we know which one is lighter / heavier. Suppose 0 1 2 is the set, weigh any 2. If they are same the other one is the answer else the one which corresponsds to the heaviness or lighterness is the answer. Weigh 3 Step 1.2 : Suppose 0 1 2 and 3 4 5 has balanced, the problem is limited to 6 7 8 9. Step 1.2.1 : Weigh any 2 in the set against 0 1. Weigh 2 Step 1.2.1.1 : If both are balanced, Step 1.2.1.1.1 : Weigh one of the other set against 0 and find the odd one out. Weigh 3 Step 1.2.1.2 : If both are not balanced, follow the same above in step 1.2.1.1.1. Weigh 3 Phew :D
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Comments (2) Post a comment

  • much easy solution

    do this:

    1) split the balls into two sets of 5.
    weigh them. One of the sets will be heavier.
    note the heavier set. you can ignore the lighter set.

    2) now make 2 sets of 2 balls each from the 5 balls.
    weigh them. If any one is heavier then note it.if both are same then the the one ball left alone is the one we need. else note the heavier.

    3) now weigh the two balls left.. you will get the heavy ball...... :)

    KUDOS !!!!!!!!

    By Anonymous on 13 Apr, 2011 Reply

    • You don't know if the ball is heavier or lighter

      You don't know if the ball is heavier or lighter, so how will this work?
      By digitalpbk on 14 Apr, 2011 Reply
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