A few candies were distributed to three people Alice, Bob, and Charlie. The sum of the reciprocals of the number of each person's candies was equal to 1. (Alice, Bob, and Charlie knew their number of candies and they knew that the sum of the reciprocals was 1, but they did not know the number of candies the other two persons had received.)
I asked Alice whether she knows the number of each person's candies and Alice said she does not know it. Also, I asked her if she knows the total number of candies and she said she does not know it.
I asked the same questions to Bob and he said that he does not know the number of each person's candies but he knows the total number of candies.
Finally, Charlie answered to the same questions that he knows not only the total number of candies but also the number of each person's candies.
What is the total number of candies?
