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Bags of coins, one different

Source: Iran 3rd round 2012-Final exam-P4

September 20, 2012
ceiling functioncombinatorics proposedcombinatorics

Problem Statement

We have nn bags each having 100100 coins. All of the bags have 1010 gram coins except one of them which has 99 gram coins. We have a balance which can show weights of things that have weight of at most 11 kilogram. At least how many times shall we use the balance in order to find the different bag?
Proposed By Hamidreza Ziarati