Three men (Jawaharlal, Ravi, and Sunil) spent an entire day picking mangoes. They had decided that they would each take an equal share of the mangoes when they were done, but at the end of the day, they were too tired to divide them up. So they all went to sleep.
In the middle of the night, Jawaharlal woke up and decided to take his share. He counted the mangoes and saw that there was one too many to divide evenly by three. So he fed that one to a monkey, took his 1/3 share, and went back to sleep.
Shortly after, Ravi awoke and decided to take his share. Of course, he had no idea that Jawaharlal had already done this. Ravi counted the mangoes and saw that there was one too many to divide evenly by three. So he fed that one to the monkey, took his 1/3 share, and went back to sleep.
Not too long after this, Sunil woke up. He thought, "I think I will take my share now." Even now, Sunil was unaware of his friends' actions. He counted the mangoes and saw that there was one too many to divide evenly by three. So he fed that one to the monkey, took his 1/3 share, and went back to sleep.
In the morning, all three men woke up and went to look at the mangoes. Now, you must know that at this point each one was embarrassed to admit what he had done during the night, and so they all just went about dividing up the mangoes that were left. Again, there was one too many. Again, they fed that one to the monkey. Again they divided the remaining mangoes into three equal piles and each took a share.
Your task is as follows:
- Find some number of mangoes that they could have originally picked, which would divide up in the way described.
- Find the SMALLEST number of mangoes which would divide in this way.
- Explain why you are sure you have found the smallest number that will work.
- Determine how many mangoes each man and the monkey received.
- Write up your work in the usual PoW format.