Consider 10 stacks of 10 coins each, where each coin weighs 10 grams. But, one of the 10 stacks is defective, and this defective stack contains the coins of 9 grams each. Find the minimum number of weights needed to identify the defective stack. | Eklavya Online

Consider 10 stacks of 10 coins each, where each coin weighs 10 grams. But, one of the 10 stacks is defective, and this defective stack contains the coins of 9 grams each. Find the minimum number of weights needed to identify the defective stack.

The solution to this puzzle is very simple. You just must pick 1 coin from the 1st stack, 2 coins from the 2nd stack, 3 coins from the 3rd stack and so on till 10 coins from the 10th stack. So, if you add the number of coins then it would be equal to 55.

So, if none of the coins are defective then the weight would 55*10 = 550 grams.

Yet, if stack 1 turns out to be defective, then the total weight would be 1 less then 550 grams, that is 549 grams. Similarly, if stack 2 was defective then the total weight would be equal to 2 less than 50 grams, that is 548 grams. Similarly, you can find for the other 8 cases.

So, just one measurement is needed to identify the defective stack.