An old chestnut, often a follow-up to the twelve coins problem, goes like this:

A year has gone by, and tax collection time has come, and each of the dozen or so minor lordlings under the King has sent in his taxes in one of the kingdom-standard leather purses. A clerk counted out the thirty 100-gram coins from each lord's payment as they were received, and the bags were set aside in the treasury until all were received. Now with your budget from the last year, you bought the treasury a nice new digital scale, accurate to 0.1 gram and with enough capacity to weigh the entire year's tax collection in a single weighing. You put all the purses in and are shocked to find, after accounting for the known weight of the purses, that the weight comes out 30 grams short.

When the King hears about this, he first asks his seer who informs him that one of the bags contains coins that weigh only 99 grams instead of the 100 grams of the standard coins. So the King asks you to determine which of the twelve bags contains the light coins, but to justify your purchase of the scale, he asks you to do it in a single weighing. How do you go about this?

Answer

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