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Which is Which II (Posted on 2012-02-15) Difficulty: 4 of 5
This is in continuation of Which is Which.

You have ten balls - five red and five black, having precisely the same shape and size. All the red balls weigh differently, i.e. one of them is very heavy, the other heavy, another is medium, another is light and the fifth very light. Each red ball has a black twin of the same weight. It is known that:

(i) A very heavy and a medium ball put together weigh as much as two heavy balls.

(ii) A heavy and a light ball put together weigh as much as two medium balls and:

(iii) A medium and a very light ball put together weigh as much as two light balls.

Determine the least number of weighings required on a balancing scale to determine which is which, given that:

(i) Each ball can only be paired with a ball of like color before weighing, but pairing a given ball with its twin is not allowed.

(ii) Each ball can also be paired with its twin (in addition to a ball of like color) before weighing.

No Solution Yet Submitted by K Sengupta    
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Question questions for clarification | Comment 1 of 4

How many balls are permitted on the balancing scale at a time?
Is it one ball versus 1 ball only OR can one weigh two balls versus 2 balls?
What is the definition of pairing? Any two balls on the same side of the balance scale, or of any one ball on each side of the balance scale? Can more than two balls be placed on one side of the balance?
For (i), by noting that a ball's twin is not allowed to be paired with its twin, does that mean by knowing the relative weight of one ball, its twin's relative weight is also known? I.e., for (i) one only needs to determine the number of weighings of five balls of the same color to know the weighings of all ten balls. 


  Posted by Dej Mar on 2012-02-16 03:35:06
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