Let us now solve the main problem. Make a collection of balls taking nx10n balls from the nth pot i.e. 10 balls from the 1st pot, 200 balls from the 2nd pot, 3000 balls from the 3rd, 40000 balls from the 4th and so on. Now use the balance and standard mass stones to weigh the total mass of the collection. Note that, if all of the 9 pots contain balls of 1.0 gram then the total mass of the above collection will be 9876543210.0 (say, trivial mass). When some of the pots contain balls of mass 1.1 gram then the total mass of the collection must differ from the trivial mass. Then the nonzero digits in the difference of total mass and trivial mass give the serial numbers of the pots containing balls of mass 1.1 gram.
For example, if 2nd, 4th, 7th and 8th pots contain the balls of mass 1.1 gram and others contain balls of mass 1.0 gram, then total mass of the aforesaid collection is
For n=1, 10x1.0 = 10.0
For n=2, 200x1.1 = 220.0
For n=3, 3000x1.0 = 3000.0
For n=4, 40000x1.1 = 44000.0
For n=5, 500000x1.0 = 500000.0
For n=6, 6000000x1.0 = 6000000.0
For n=7, 70000000x1.1 = 77000000.0
For n=8, 800000000x1.1 = 880000000.0
For n=9, 9000000000x1.0 = 9000000000.0
Total mass = 9963547230.0
Here the difference of total mass and trivial mass is 9963547230.0 - 9876543210.0 = 87004020.0. Therefore, the nonzero digits 2, 4, 7 and 8 in the number 87004020.0 give the serial numbers of the required pots.