a woman has some peanuts. she sees a friend at the door and she quickly eats a peanut before her friend enters and takes one-half of the remaining peanuts. she sees another friend at the door and she quickly eats another peanut before the second friend enters and takes one-half of the remaining peanuts. Finally, she sees a third friend at the door and she eats another peanut before the third friend enters and takes on half of the remaining peanuts, leaving her with only one peanut. How many peanuts did the woman originally have?