10 packets of cigarettes

Question: 

You have 10 packets of cigarettes and each packet contain 10 cigarettes. We assume that the packets are weightless and that each cigarette weigh 10 grams. But in one of packs every cigarette weighs 1 gram extra (i.e. 11 grams) and thus that pack weighs 110 grams. We don’t know which pack is culprit. We have electronic weighing machine ( not usual one with two panes) and we need to figure out that pack. How can we figure out? The only condition in the question is: You can use the weighting machine only once to weigh.

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Solution:

Take one cigarette out of the first pack, two cigarettes out of the second pack, three cigarettes out of the third pack, four out of the fourth pack and so on. Then place all of them in the balancer. In Ideal situation, the weight should be

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

But if any of the counts belongs to that faulty pack it will create that much amount of extra grams. For example, we took out 4 cigarettes out of the fourth pack and that is the one which is faulted then it will increase the weight by 4 grams. So if the weight is extra by n grams then the nth pack is the one we need to find.

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