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## #1 2006-03-01 13:42:43

Math Guy
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### A Farmer, a Daughter — and an Unknown Number of Apples

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!!!!!!

## #2 2006-03-01 23:03:08

MathsIsFun

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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

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

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #3 2006-03-03 21:47:18

Zach
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

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.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #4 2006-03-04 04:39:02

mathsyperson
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

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.

Why did the vector cross the road?
It wanted to be normal.

## #5 2006-03-04 06:10:38

espeon
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

8?

Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

## #6 2006-03-04 07:06:06

Patrick
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

edit: nvm

Last edited by Patrick (2006-03-04 07:09:29)

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## #7 2006-03-06 20:39:15

Zach
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

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

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #8 2006-03-07 06:28:15

espeon
Real Member

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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

8 and get someone to cut the apple for him

Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

## #9 2006-03-07 12:41:59

Math Guy
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

15 is correct, congrats!

## #10 2006-03-07 19:14:16

Zach
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

Liez.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #11 2006-03-08 03:32:18

mathsyperson
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### Re: A Farmer, a Daughter — and an Unknown Number of Apples

#### Zach wrote:

Liez.

Liez.

Why did the vector cross the road?
It wanted to be normal.