Three hungry men and strategies for problem solving

Sometimes a problem starts out innocently, like the prover­bial mustard seed; but then it starts to grow and, Zap, you are engulfed by a mustard tree! So it was with the Three Hungry Men problem:

Three tired and hungry men went to sleep with a bag of apples. One man woke up, ate 1/3 of the apples, then went back to sleep Later a second man woke up and ate 1/3 of the remaining apples, then went back to sleep Finally, the third man woke up and ate 1/3 of the remaining apples. When he was finished there were 8 apples left How many apples were in the bag originally?