Chapter 6.2, Problem 15P

Three robbers have just acquired a large pile of gold coins. They go to bed, leaving their faithful servant to guard it. In the middle of the night, the first robber gets up, gives 2 gold coins from the pile to the servant as hush money, divides the remaining pile of gold evenly into 3 parts, takes 1 part, forms the remaining 2 parts back into a single pile and goes back to bed. A little later, the second robber gets up, gives 2 gold coins from the remaining pile to the servant as hush money, divides the remaining pile evenly into 3 parts, takes 1 part, forms the remaining 2 parts back into a single pile and goes back to bed. A little later, the third robber gets up and does the very same thing. In the morning, when they count up the gold coins, there are 100 of them left. How many were in the pile originally? Explain your answer.