DAY 412

A fruit seller has a basket of oranges. His first customer buys half the oranges plus half an orange. The next customer buys half of what's left plus half an orange. The last customer buys half of what's left plus half an orange, leaving the basket empty. No oranges were cut or broken in any way. How many oranges did the fruit seller start with?

Answer:

Problems like these can be solved with algebra, but a simpler solution is possible. Since the problem tells us no oranges were cut or broken, we know that only whole oranges were sold to the customers. The "half" orange must be used to complete a whole orange - as in 1 1/2 + 1/2 = 2. The only way to take half of a number and add 1/2 to it to get a whole number, is to start with an odd number. 

In this problem, since there were only three transactions before the basket was emptied, there could not have been that many oranges. Thinking of the odd numbers - 1, 3, 5, 7, 9, 11 ............... 7 oranges solves the problem:

First customer: 3 1/2 (half of seven) + 1/2 = 4 (leaving 3)
Second customer: 1 1/2 (half of three) + 1/2 = 2 (leaving 1)
Third customer: 1/2 (half of one) + 1/2 = 1 (leaving 0)