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Answer to old chestnut: N bags of coins:

Label the bags 1 to N, and put 1 coin from bag 1, 2 coins from bag 2, 3 coins from bag 3, ..., N coins from bag N onto the scale. The difference between the weight shown and the weight that that number of good coins would weigh tells you how many bad coins are on the scale, and thus which bag is light.

For instance, if there were 6 bags, you would put 1+2+3+4+5+6 = 21 coins on the scale, and expect the weight to come out to 2100 grams if the coins were all good. If the weight is 2096 grams, you know 4 of the coins are light, and the 4th bag has the bad coins.

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