4
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A party is being held at a local mansion. The host is very rich and his success is because of one thing — his famous recipe for Spaghetti!

The only guests that may attend are people who correctly reply to the guard at the door.

Here's where you come in. You and a friend are trying to steal this recipe. You sneak by and listen to the passwords.

The first guest arrives. The guard says, "1", the guest replies "2" and is let in.

The second guest arrives. The guard says, "3", the guest replies "5" and is let in.

The third guest arrives. The guard says, "8", the guest replies "4" and is let in.

Your friend says, "Aha! This is an easy one." He slips away and show up at the gate a minute later. "13", the guard says. Your friend replies "3" and is immediately trampled by an elephant.

Where did your friend go wrong?

Hint:

You decide to hang around a bit longer. The next guest arrives, and the guard says, "2". The guest replies "2" and is let in.

Second Hint:

Another guest arrives, and the guard says "89". The guest replies "8" and get in.

Final hint:

Still scratching your head, you wait for another guest to approach. "Two" you hear the guard start to say, but at that exact moment a passing truck honks somewhere behind you, nearly startling you out from the tree. You barely recover in time to hear the guest reply, "8" and the guard lets her in.

Having read the above hints, now you decide to approach the guard. He says, "34", what do you reply?

As usual please post your answer, an explanation of what process you used to get the answer and any hints used in spoiler tags.

Note: Whoops, flubbed the final hint. It should be correct now.

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closed as off-topic by Gilles, Florian F, Joe Z., Psychemaster, Rob Watts Nov 17 '14 at 20:58

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  • 1
    $\begingroup$ this is complex, even with all the hints I can't solve it $\endgroup$ – Rafe Nov 12 '14 at 21:02
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    $\begingroup$ @Victor has mentioned the Fibonacci series. That was great. and my guess is that "Two...." is 233, 12th number of the series. (or with low probability, 2584) $\endgroup$ – Rafe Nov 12 '14 at 21:05
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    $\begingroup$ @Rafe, yeah, got to the same conclusion. However no matter what I do, I can't make sense of the numbers. Already tried counting the letters of its Fibonacci position, but that fails for 89 and "two..." $\endgroup$ – Victor Stafusa Nov 12 '14 at 21:08
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    $\begingroup$ I gave up and going to bed! happy puzzling @Victor $\endgroup$ – Rafe Nov 12 '14 at 21:19
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    $\begingroup$ I don't get why 233 and 89 have the same result.. My brain starting to hurt.. :< $\endgroup$ – Emi987 Nov 12 '14 at 21:23
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Ok Here's my friends try:

34 = 7

1=2

2=2

3=5

5=8

8=13=1+3=4

13=4

21=3

34=7
...
89=8+9=17=1+7=8 How it works: The number given is one of Fibonacci numbers If it have 1 char => return next number from Fibonacci If it have 2 char => plus them together

And now 21 is not 3, I guess luckily the guard didn't give me 21 :D

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  • $\begingroup$ I think that you got it. $\endgroup$ – Victor Stafusa Nov 14 '14 at 13:11
  • $\begingroup$ Everything is right except for one thing: the correct response to 21 is not 3. $\endgroup$ – Michael Nov 14 '14 at 15:30
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    $\begingroup$ It might help to more explicitly state the general relationship between the numbers, instead of just enumerating it for each input. $\endgroup$ – Michael Nov 14 '14 at 21:48
  • $\begingroup$ I really don't know how to make that text shade .... $\endgroup$ – Cường Nguyễn Nov 15 '14 at 2:06
  • $\begingroup$ Your explanation is not quite correct, which is why you aren't getting the right response for 21. $\endgroup$ – Michael Nov 15 '14 at 3:19
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Most patterns I'm getting seem to point me at

7, but I can't find the pattern that fits perfectly.

I know it's got to have something to do with the Fibonacci numbers and particularly their indices in the series, but I just can't seem to crack it...

Another hint maybe?

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    $\begingroup$ That's the correct answer to 34, but can you tell me why? $\endgroup$ – Michael Nov 12 '14 at 23:28
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    $\begingroup$ It was the only answer that seemed to match the patterns of the others, given that 8 was deemed incorrect (so I cheated!) My closest guess was that the answer was the corresponding index of the given number in sequence, minus an amount equal to the number of digits of the initially given number. But that only matched up for about half or so of the given scenarios... $\endgroup$ – Chris Sprague Nov 13 '14 at 3:15
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My answer:

The guard always asks a number from the Fibonacci series:

[1 -> 1, 2 -> 2, 3 -> 5, 5 -> ???, 8 -> 4, 13 -> ??? (not 3), 21 -> ???, 34 -> ???, 55 -> ???, 89 -> 8]

2 is the 2nd answer of the series, which maps to a value that is the double of the 1st answer.

89 is the 10th answer of the series, which maps to 8, the double of the 5th answer, which is 4.

The answer for 34 should be the double of the answer for 5, which is the double of the answer of 2.

So the answer is 8.

EDIT: Wrong answer! I was trampled by an elephant. :(

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    $\begingroup$ You are definitely on the right track, but haven't got all the details quite right, and your answer to "34" is incorrect. $\endgroup$ – Michael Nov 12 '14 at 20:10
  • $\begingroup$ If I could do a >! spoiler in a comment I would add an extra hint "just" for you (or anyone reading your answer). $\endgroup$ – Michael Nov 12 '14 at 20:10
  • $\begingroup$ Ok, put it in question. If you think it might be too easy, try to produce a harder one, even if it is in the form of "you couldn't understand what the guard did said, because a truck in the street honked just in that moment, but the answer given by the guest was X". $\endgroup$ – Victor Stafusa Nov 12 '14 at 20:16
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    $\begingroup$ Trunk honking that's great! I've added a final hint. $\endgroup$ – Michael Nov 12 '14 at 20:22
  • $\begingroup$ Whoops, re-read the updated final hint, I flubbed it the first time. $\endgroup$ – Michael Nov 12 '14 at 20:38

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