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In a temple, there were three beggars. A pilgrim came to the temple with few coins. The pujari of the temple gave him a magic bag in which coins get trippled each time you put that coins into it. He put all the coins he had in that bag and the coins got trippled. He took out all the coins and gave few to the first beggar and then again put the remaining coins back in the bag. The coins got trippled again; he took out all the coins again and gave few coins to the second beggar. He then again put the remaining coins in the bag and the coins got trippled again. He took out all the coins and gave few coins to third beggar. There were no coins left with him when he gave coins to third beggar and he gave equal number of coins to each beggar. How many coins did he gave to each beggar?

Question

In a temple, there were three beggars. A pilgrim came to the temple with few coins. The pujari of the temple gave him a magic bag in which coins get trippled each time you put that coins into it. He put all the coins he had in that bag and the coins got trippled. He took out all the coins and gave few to the first beggar and then again put the remaining coins back in the bag. The coins got trippled again; he took out all the coins again and gave few coins to the second beggar. He then again put the remaining coins in the bag and the coins got trippled again. He took out all the coins and gave few coins to third beggar. There were no coins left with him when he gave coins to third beggar and he gave equal number of coins to each beggar. How many coins did he gave to each beggar?

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Solution

Let's solve this step by step:

  1. Let's assume the number of coins each beggar received is x.

  2. According to the problem, the pilgrim gave away all his coins to the third beggar after tripling them for the third time. This means after the third tripling, he had x coins.

  3. Before the third tripling (and after giving some coins to the second beggar), he must have had x/3 coins.

  4. Before giving coins to the second beggar (and after the second tripling), he had x + x/3 = 4x/3 coins.

  5. Before the second tripling (and after giving some coins to the first beggar), he must have had (4x/3) / 3 = 4x/9 coins.

  6. Before giving coins to the first beggar (and after the first tripling), he had x + 4x/9 = 13x/9 coins.

  7. Therefore, initially, before the first tripling, he must have had (13x/9) / 3 = 13x/27 coins.

Since the number of coins must be a whole number, x must be a multiple of 27. Given that the pilgrim had "a few" coins, we can assume that x = 27 is a reasonable solution.

So, each beggar received 27 coins.

This problem has been solved

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