Something for the Marmalade

       A little girl I know sells oranges from door to door.

One day while on her rounds she sold ½ an orange more than half her oranges to the first customer. To the second customer she sold ½ an orange more than half of the remainder and to the third and the last customer she sold ½ 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.

Answer:  In order that the little girl should have disposed of the oranges she had remaining after her second sale, she must have had at least one whole orange remaining so that she could deduct from it ‘half of her oranges plus half an orange’, for the third and the remaining so that she could deduct from it’ half of her oranges plus half an orange represents half of the remaining after the second sale, then she must have sold two oranges in her second sale. Leaving the 3 oranges after the first sale.

Lastly, if three oranges only represent half the original number, plus half an orange, then she must have started with [(3 ×2) + 1] or 7 oranges.