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"Those danged pirates!" Captain Crackskull sighed. "You'd think they'd get their fill and just leave people alone, but noo-o-ooo, even with all their GPS navigation systems and personal gadgetry, they're still just pirates, stuck in their piraty ways. Arrrh. They get more loot than they know how to spend and they just bury it. The only thing that's changed is that they bury their treasure in electronic vaults instead of caves."

Prying a PDA from the skeletal hand of some poor old sailor who hadn't been given a decent burial, he charged it up and began poking around. It showed the word IBAN, followed by a series of letters and numbers. The captain punched it into a website. "Lazy." He shook his head. "It's a valid bank account number. We just need to figure out what he used for a password."

He found something scratched on the back of the PDA.

1-6: 0, 1, 3, 6, 10, _, _, _

7-12: 0, -1, -1, -1, 0, 2, 6, 13, _, _, _

13-17: 3, 4, 5, 5, 6, 14, _, _, _

"Hmmm. You think I'd be better at these, but I'm still busy trying to solve half a dozen other ones. I'm happy to split the booty with you if you can solve it."

Edited by Phatfingers
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could you give a hint on the last one. its not coming to me

You pick up the PDA and find that the dead pirate kept a journal. Apparently, he dropped out of school when he was only 7 and didn't learn any additional math beyond that grade level. How sad. He didn't seem to be keen on the concept of encoding or translating numbers taken from non-numeric elements-- he was just purely a simple, straight numbers guy.

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Could you post how you arrive at these answers with your guesses? I am looking at the second one - and it still eludes me. Got the first one, but someone beat me to it... :(

Thanks!

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Could you post how you arrive at these answers with your guesses? I am looking at the second one - and it still eludes me. Got the first one, but someone beat me to it... :(

Thanks!

Sure. Here's at least one way to arrive at the answers.

With N starting at 0:

S[0] = 0

S[N] = S[N-1] + N

Add 1, then 2, then 3, etc.

You're probably familiar with the Fibonacci sequence:

F[1] = 1

F[2] = 1

F[N] = F[N-2] + F[N-1]

N = 1, 2, 3, 4, 5, 6, ...

F[N] = 1, 1, 2, 3, 5, 8, ...

Series 7-12 = F[N] - N

Ha, ha. Made you look.

Clues suggest that it uses math a 2nd grader can perform, and that it doesn't need anything outside the realm of math.

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"I'm pretty sure I correctly figured the first two parts of the dead pirate's password," you confide to the Captain, "but I'm not sure how to approach that third sequence. It doesn't seem to conform to a regular pattern."

"What do yer mean?"

"I tried graphing it, and while the numbers appear to increase, they don't follow any sort of line or curve. They almost seem, well... random."

"Let me see that," he says. "Hmm."

"What?"

"Oh, it may be nothing, but I find that many of these series seem to start with a 0, 1, or maybe 2."

"So?"

"This one starts with a three. That may mean something. It's not heading towards a pattern of threes, like 3, 6, 9, or such, so maybe there's something significant about the use of three as a starting point. Where did the pirate get that three?"

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17, 18, 19, 19, 20?

(just add 3 to the last given # in the sequence and repeat?)

The answer will exactly fill the five digits, 13-17, of the numeric password. One of them must be a single-digit number.

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...

"So?"

"This one starts with a three. That may mean something. It's not heading towards a pattern of threes, like 3, 6, 9, or such, so maybe there's something significant about the use of three as a starting point. Where did the pirate get that three?"

You ponder this over and over in your head. Mmmm. Sort of random. Starts with three. You're distracted momentarily by something cooling in the windowsill...

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You ponder this over and over in your head. Mmmm. Sort of random. Starts with three. You're distracted momentarily by something cooling in the windowsill...

3 = 3

3 + 1 = 4

1 + 4 = 5

4 + 1 = 5

1 + 5 = 6

5 + 9 = 14

9 + 2 = 11

2 + 6 = 8

6 + 5 = 11

5 + 3 = 8

etc...etc...

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