SOLUTION: a man passed through into an orchard, where he picked a certain number of apples. On the way out of the orchard, he gave the first guard half of the apples that he had and one more

Question 163712: a man passed through into an orchard, where he picked a certain number of apples. On the way out of the orchard, he gave the first guard half of the apples that he had and one more. He gave the second guard half of the remaining apples and one apple more. He did the same for each of the remaining five guards and finally left the orchard with one apple. How many apples did he pick in the orchard?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!



Pretend that a video was made of the whole thing.

Now let's pretend to show that video backwards.

We see the man walking backward up the the 5th guard holding 
1 apple. The 5th guard gives the man 1 apple, making him have 
2 apples. Then the 5th guard gives him 2 more, so that when 
he walks backward away from the 5th guard towards the 4th 
guard he has 4 apples.

He then walks backward up the the 4th guard holding 4 apples.
The 4th guard gives the man 1 apple, making him have 5 apples.
Then the 4th guard gives him 5 more, so that when he walks backward 
away from the 4th guard towards the 3rd guard he has 10 apples. 

He then walks backward up the the 3rd guard holding 10 apples.
The 3rd guard gives the man 1 apple, making him have 11 apples.
Then the 3rd guard gives him 11 more, so that when he walks backward 
away from the 3rd guard towards the 2nd guard he has 22 apples.

He then walks backward up the the 2nd guard holding 22 apples.
The 2nd guard gives the man 1 apple, making him have 23 apples.
Then the 2nd guard gives him 23 more, so that when he walks backward 
away from the 2nd guard towards the 1st guard he has 46 apples.

He then walks backward up the the 1st guard holding 46 apples.
The 1st guard gives the man 1 apple, making him have 47 apples.
Then the 1st guard gives him 47 more, so that when he walks backward 
away from the 1st guard towards the the orchard he has 94 apples.
He then puts the 94 apples back on the trees. J

So the answer is that he picked 94 apples before reaching the 1st 
guard.

Checking:

He picked with 94 apples.
He gave the 1st guard half of 94, or 47, plus 1 apple.
That is, he gave the 1st guard 48 apples.
Then he walked away from the 1st guard with 94-48 or 46 apples.

Then he gave the 2nd guard half of 46, or 23, plus 1 apple.
That is, he gave the 1st guard 24 apples.
Then he walked away from the 2nd guard with 46-24 or 22 apples.

Then he gave the 3rd guard half of 22, or 11, plus 1 apple.
That is, he gave the 1st guard 12 apples.
Then he walked away from the 3rd guard with 22-12 or 10 apples.

Then he gave the 4th guard half of 10, or 5, plus 1 apple.
That is, he gave the 1st guard 6 apples.
Then he walked away from the 4th guard with 10-6 or 4 apples.

Then he gave the 5th guard half of 4, or 2, plus 1 apple.
That is, he gave the 1st guard 3 apples.
Then he walked away from the 5th guard with 4-3 or 1 apple.

So that's the correct answer, 94.

Edwin

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