#### Posers and Puzzles

JS357
Posers and Puzzles 22 Feb '16 22:48
1. 22 Feb '16 22:48
There is an avocado tree surrounded by seven concentric fences, each with a gate that is guarded by a soldier. The soldiers are known for their honesty and so are you. You love avocados. You go up to the first guard and tell him that if he lets you pass through his gate, you promise that you will give him half of the avocados you have when you return to his gate, on condition that he then give you one back and let you pass. You will only deal with whole avocados. He agrees and lets you pass.

You go to the second guard and make this same deal. In fact, you go to all the guards, one at a time, and make the same deal.

How many avocados should you take from the tree to be able to deliver on your promise?

2. wolfgang59
Mr. Wolf
23 Feb '16 20:441 edit
Originally posted by JS357
There is an avocado tree surrounded by seven concentric fences, each with a gate that is guarded by a soldier. The soldiers are known for their honesty and so are you. You love avocados. You go up to the first guard and tell him that if he lets you pass through his gate, you promise that you will give him half of the avocados you have when you return to his ga ...[text shortened]... le to deliver on your promise?

There are many answers but I'm guess you are looking for the minimum?
[hidden]
Taking 130 ensures no soldier is peed off.
But the minimum is 2, with every soldier ending up with zero avocados.
[/hidden]
3. 23 Feb '16 23:05
Originally posted by wolfgang59
There are many answers but I'm guess you are looking for the minimum?
[hidden]
Taking 130 ensures no soldier is peed off.
But the minimum is 2, with every soldier ending up with zero avocados.
[/hidden]
Two is the answer and it is the only answer. Any other number results eventually in having to give half of an odd number of avocados.

I was hoping someone would say Avogadro's number.
4. sonhouse
Fast and Curious
24 Feb '16 12:13
Originally posted by JS357
[hidden]Two is the answer and it is the only answer. Any other number results eventually in having to give half of an odd number of avocados.[/hidden] <-- answer

I was hoping someone would say Avogadro's number.
I missed the part where the guard gives back one avocado. So with your result, none of the guards gets a single avocado! You end up with 2.
5. 24 Feb '16 14:19
Originally posted by sonhouse
I missed the part where the guard gives back one avocado. So with your result, none of the guards gets a single avocado! You end up with 2.
Yes but now I'm not sure Wolfgang's 130 is wrong.

After gate 1: 66

After gate 2: 34

After gate 3: 18

After gate 4: 10

After gate 5: 6

After gate 6: 4

After gate 7: 3.

And there are other answers, such as starting with the number that yields 130 AFTER gate 1. That is 258.

Is this right?

I got this from the NPR program Cartalk.
6. sonhouse
Fast and Curious
24 Feb '16 14:51
Originally posted by JS357
Yes but now I'm not sure Wolfgang's 130 is wrong.

After gate 1: 66

After gate 2: 34

After gate 3: 18

After gate 4: 10

After gate 5: 6

After gate 6: 4

After gate 7: 3.

And there are other answers, such as starting with the number that yields 130 AFTER gate 1. That is 258.

Is this right?

I got this from the NPR program Cartalk.
Loved that show. Tom, RIP. He had a good run, Phd, and his younger brother Ray graduated from MIT. Pretty good pedigrees.
7. 24 Feb '16 15:45
Originally posted by sonhouse
Loved that show. Tom, RIP. He had a good run, Phd, and his younger brother Ray graduated from MIT. Pretty good pedigrees.
You can listen to reruns on the cartalk website. We have them on KQED on Saturday. They seem to be from the 90's judging by the model years being discussed.
8. sonhouse
Fast and Curious
24 Feb '16 17:49
Originally posted by JS357
Yes but now I'm not sure Wolfgang's 130 is wrong.

After gate 1: 66

After gate 2: 34

After gate 3: 18

After gate 4: 10

After gate 5: 6

After gate 6: 4

After gate 7: 3.

And there are other answers, such as starting with the number that yields 130 AFTER gate 1. That is 258.

Is this right?

I got this from the NPR program Cartalk.
That series looks like a famous one, like a fibonacci number sequence almost.
9. 24 Feb '16 22:35
Originally posted by sonhouse
That series looks like a famous one, like a fibonacci number sequence almost.
Divide by two, add one. Repeat. Any number can be tested (brute force) to see if an odd number is reached before 7 tries. Is there a mathematical way; solving for x =130.?

In reverse it is double then subtract 2.

eg (2*3)-2=4, (2*4)-2=6

Starting with 5 it is 5, 8, 14... so from 8 on, even numbers result.

Same with 7.

I seems there is an unlimited number of solutions.
10. wolfgang59
Mr. Wolf
26 Feb '16 08:34
Originally posted by wolfgang59
There are many answers but I'm guess you are looking for the minimum?
[hidden]
Taking 130 ensures no soldier is peed off.
But the minimum is 2, with every soldier ending up with zero avocados.
[/hidden]
WHY DOES MY "HIDDEN" NOT WORK? ðŸ˜
11. sonhouse
Fast and Curious
26 Feb '16 16:43
Originally posted by wolfgang59
WHY DOES MY "HIDDEN" NOT WORK? ðŸ˜
It does work, start with two, you give one to a guard, he gives you one back. You still have 2, all the way through no matter how many guards there are. You end up with two avocado's. The other solutions seem to give you more avocado's at the end. Although how you would carry 130 avocado's in the first place is unclear.....
12. wolfgang59
Mr. Wolf
26 Feb '16 22:33
Originally posted by sonhouse
It does work, start with two, you give one to a guard, he gives you one back. You still have 2, all the way through no matter how many guards there are. You end up with two avocado's. The other solutions seem to give you more avocado's at the end. Although how you would carry 130 avocado's in the first place is unclear.....
?????? ðŸ™„

[ hidden ] in my post didn't work!
13. 26 Feb '16 23:30
Originally posted by wolfgang59
WHY DOES MY "HIDDEN" NOT WORK? ðŸ˜

[hidden]
Taking 130 ensures no soldier is peed off.
But the minimum is 2, with every soldier ending up with zero avocados.
[/hidden]

Here it is with the carriage returns removed.

Taking 130 ensures no soldier is peed off. But the minimum is 2, with every soldier ending up with zero avocados.
14. wolfgang59
Mr. Wolf
27 Feb '16 20:42
Originally posted by JS357

[hidden]
Taking 130 ensures no soldier is peed off.
But the minimum is 2, with every soldier ending up with zero avocados.
[/hidden]

Here it is with the carriage returns removed.

[hidden]Taking 130 ensures no soldier is peed off. But the minimum is 2, with every soldier ending up with zero avocados.[/hidden]
thanks - mystery solved!
15. 28 Feb '16 01:13
Originally posted by wolfgang59
thanks - mystery solved!
"Carriage return" is such a quaint term. I wonder what other terms that we use are vestiges of a previous technology.