You have ten stacks of ten coins each and each of them weighs 10 gm. However, one of the stacks is faulty and each of the coins in it weighs only 9 gms. What is the least number of times you have to weigh to find the faulty coin?
The least number of times you have to weigh is just once! Line up the stacks and pick 1 coin from first stack, 2 coins from second stack, 3 coins from third stack and so on. You will have a total of 55 coins. Now weigh it. If all of them were the right weight, the total would be 550 gms. If the total is 549, the first stack is faulty; if the total is 548 then the second stack is faulty and so on.
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