A little girl I know sells oranges from door to door. One day while on her rounds she sold half an orange more than half her oranges to the first customer. To the second customer she sold half an orange more than half of the remainder and to the third and the last customer she sold half an orange more than half she now had, leaving her none. Can you tell the number of oranges she originally had? Oh, by the way, she never had to cut an orange.