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# Gold Coin Barrels(2)

There are 10 barrels of gold coins. In that, some of the barrels contain 1 gram gold coins and some of the barrels contain 2 gram gold coins. There is a weighing machine which is allowed to weigh only once. Which of the barrels contain 2 gram coins?

## Answers : Math Puzzles and Riddles

 There are 10 barrels totally. Let's take the coins from the barrel in the power of 2. Take 1 coin 20 from first barrel, 2 coins 21 from first barrel, 4 coins 22 from first barrel, as on for ten barrels till 512 coins 29. Now consider that if every barrel contains 1 gram coins, the total weight of the coins picked from the barrels will be 1023 grams.        In this many of the barrel contains 2 gram coins, so we would have to subtract repeatedly from the last. For example, if the weight was 1289 grams. First subtract from the considered weight 1023 from the total weight. Now the value will be 266. Now take the nearest equal power which is less than or equal to the value. 256 is the largest number that is less than 266, so note that 8th barrel contains 2 gram gold coins. Now subtract 256 from 256, 10 will be the value. Again see the nearest equal value. 8 is less than the value, so note that the barrel 4 contains the 2 gram gold coins. At last subtract 8 from 10, 2 will be the value. 2 is equal to the barrel 2. Finally the 2 gram coins are on 2, 4 and 8 barrels.

There are 10 barrels of gold coins. In that, some of the barrels contain 1 gram gold coins and some of the barrels contain 2 gram gold coins. There is a weighing machine which is allowed to weigh only once. Which of the barrels contain 2 gram coins?

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