A farmer has to make eight stops in delivering eggs. He begins with exactly the number of eggs he needs for these eight deliveries. At the first app he delivers half of the eggs he has +1/2 of an egg. At each of the next seven stops he delivers half of the remaining eggs plus half of an egg. When he is finished he has no eggs left, and none have been broken when making the deliveries. How many eggs did he have any began his deliveries?