A Farmer, a DaughterÃ¢â‚¬â€And an Unknown Number of Apples
RAY: If he has to wind up with one apple for the daughter, then at the last fence post he had to have approached that fence post with three apples in his hand, because he gave half of his apples and another half to the fence post. Half of his apples were one and a half.
TOM: I'm with you.
RAY: And another half is --
TOM: Two. And he's got one left, so he started with three.
RAY: If you work backwards, at the fence post before that he had to have seven. So we approach that fence post with seven. He left half of those, which was three and a half-- plus a half.
That's how he wound up with the three. He started out with seven, left four behind.
Repeat this step one more time, and you'll see, what? He left the orchard with 15 apples.
TOM: I guessed 13. I was close.
RAY: You were perilously close. Do we have a winner?
TOM: Yes, we do. The winner this week is Tim Croft from Snellville, Georgia, and for having his answer selected at random from among all the correct answers that we got, Tim is going to get a 26 Ã¢â‚¬â€œdollar gift certificate to the Shameless Commerce Division at Car Talk.com with which he can get a beautiful gold, blue and white Car Talk football jersey. Blood and grass stains are sold separately.
[ Car Talk Puzzler ]