A Farmer, a Daughter and an Unknown Number of Apples

Math Guy · 2006-02-28 14:42:43

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?

*Leave what you think is the right answer here, guessing never hurts!!!!!!

MathsIsFun · 2006-03-01 00:03:08

I see, so when he leaves "half the apples plus half an apple more" he is not allowed to leave an actual "half" of an apple.

So, if he has 15 apples, he could leave 7½ plus ½ = 8

Zach · 2006-03-02 22:47:18

16 - 8 + 1 = 7 - 4 = 3 - 2 = 1

He goes to the field and picks 16 apples. At gate 1, he leaves 9 to leave him with a total of 7 apples. At gate 2, he leaves the right amount; 4 apples to leave him with 3. At the final gate, he also leaves the correct amount; 2 apples to leave him with a single apple.

mathsyperson · 2006-03-03 05:39:02

Very close. You just made a slight mistake with the first stage. Half of 16 is 8, and so after leaving half more, he would have 7 1/2 apples left.

espeon · 2006-03-03 07:10:38

8?

Patrick · 2006-03-03 08:06:06

edit: nvm

Last edited by Patrick (2006-03-03 08:09:29)

Zach · 2006-03-05 21:39:15

He can't half an apple, so he must leave 9 apples.

espeon · 2006-03-06 07:28:15

8 and get someone to cut the apple for him

Math Guy · 2006-03-06 13:41:59

15 is correct, congrats!

Zach · 2006-03-06 20:14:16

Liez.

mathsyperson · 2006-03-07 04:32:18

Zach wrote:

Liez.

Liez.

Math Is Fun Forum

#1 2006-02-28 14:42:43