A Farmer, a Daughter—And an Unknown Number of Apples

Feb 27, 2006

RAY: As luck would have it, this puzzler was sent in by two different people, a week apart. A fellow named Ronald Byas and another fellow named Milton Mercinger both sent in basically the same puzzle. I kind of mixed them together.

TOM: Did you obfuscate?

RAY: Of course! Here it is:

A young man wants to ask a farmer for his daughter's hand in marriage. In fact, he wants more than the hand, he wants the whole girl. And the farmer says, "If you do this right, I'll give you her, a few cows, and I'll throw in a tractor!"

TOM: And my wife, too!

RAY: "But in order to have her hand in marriage, I want you to walk out to the apple orchard and pick some apples. On your way back to the farmhouse, you're going to pass three fence posts. At the first one, you're going to leave half the apples you have, and half an apple more. When you get to the second fencepost, you're going to do the same thing: leave half the apples that you have remaining, and half an apple more. You'll do the same thing at the third fencepost.

"You can't cut, bite, fold, spindle, mutilate, or do anything to any of the apples. But, you must, when you're all done, have one apple remaining for my daughter. If you can do that, you can marry her, or you can have the tractor, whichever you want."

The question is, how many apples does the young man need to pick from the orchard so that when he starts out he has x number of apples, and when he's all done leaving half the apples plus half an apple at each of the three fence posts, he has one left?
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.

TOM: Right.

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 –dollar 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.

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