Which One is Heavier? - Answer

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Which One is Heavier? 

- Answer

Age group: All

The question was:

"You have 9 marbles: 8 of them weigh 1 gram each; 1 weighs 1.1 gram. The 9 marbles are all uniform in size, appearance and shape. You have access to a balance scale containing 2 trays - you may use the balance twice.

You must determine which of the 9 marbles is the heavier one using the balance only twice."


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Now coming to the Answer!

The important point to keep in mind here is that the balance can be used only twice.

There are a total of 9 marbles, and we must divide them in such a way that we can compare all balls in 2 uses of the balance.

The way to go is as follows:
  1. Divide the 9 marbles into groups of 3.
  2. Let the groups be A (containing marbles A1, A2, A3), B (containing marbles B1, B2, B3) and C (containing marbles C1, C2, C3).
  3. Take any two groups and keep each group on opposite scales in the balance. Let the groups taken be A and B.
  4. The side towards which the balance inclines indicates that that group of marbles contains the heavier marble (i.e. if the balance inclines towards group A then one of the three marbles in A is heavier).
  5. If the balance is perfectly balanced, then it is the third group of marbles that hadn't been placed on the balance that has the heavier marble (i.e. one of the three marbles in C is heavier).
  6. Taking the heavier group after steps 4 and 5 (say C), take 2 marbles from that group of three marbles (say C1 and C2) and place each on the opposite scale of the balance.
  7. The side towards which the balance inclines indicates that marble is heavier (i.e. if the balance inclines towards group C1 then C1 is heavier).
  8. If the balance is perfectly balanced, then it is the third marble that had not been placed on the balance the second time that is heavier (i.e. C3 is heavier).
This way, you can determine the heavier marble by using the balance only twice!

***

If you have got the same answer in any other way, then do let me know in the comments section!

If you have interpreted this question in another suitable way, then do let me know in the comments section again!

If I have made any significant errors, do let me know about that too, and I will be sure to make the necessary changes!
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I hope you enjoyed this :)


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With Warm Wishes,
Lavanya

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