Pete Wheels is a used car salesman. He sold half his cars plus one more to his first customer of the day. To the second customer, he sold half of the remaining plus one more. To the third customer, he sold half the remainder plus one more; and to the fourth customer, he sold half the remainder plus one more. Pete was now the proud salesman of an empty car lot. How many cars did Pete have for sale at the start of the day?
Answer
Thirty. The trick is to work backwards. On his fourth and final sale, he sells half of his remainder plus one more, leaving him with zero. Therefore, we know that he sold one plus one more on the fourth sale. On the third sale, he sold half of six, plus one more which left him with two for the fourth sale. On the second sale, he sold half of 14 plus one more which left him with six for the third sale. Therefore, on the first sale he sold half of 30 plus one more which left him with 14 for the second sale.
