[unreality]

After buying groceries for his mom, who turned out to be an undercover Government agent, Quaddy was kidnapped by a group of rebels posing as the Axion Police, who attempted to question Quaddy about the number sequences his mother was passing on to the Government via a contact at the grocery store. But Quaddy wasn't so cooperative... [if you want just the puzzle, skip down to the bottom of this post ]

"Look!" he shouted, pointing wildly. "An uncommon denominator!" The rebel wasn't fooled nor amused. Another person stepped into the warehouse and suggested, "Take him to the Perfect Cube."

The other rebel nodded and the two pulled out scissors, undoing Quaddy's bonds and manhandling him across the warehouse, down a flight of rusting metal stairs and through a solid titanium door... into a perfect cube.

"You'll soon be talking!" they laughed, slamming the door shut. The door merged so seamlessly with the smooth titanium walls of the cube that Quaddy was suddenly discombobulated and claustrophobic. After a few sweaty seconds of turning and mumbling, he had no idea where the door was.

Then the Cube began to spin. It whirled in all directions, tossing Quaddy around like a rag doll, blood whooshing to one side of his brain and then the other, his bones cracking with the continual impact of slamming into walls.

When the Cube finally stopped spinning, Quaddy was surrounded in blood and vomit. He was so dizzy that he didn't notice the door opening and men dragging him out, dragging him down the hall, dragging him into another room where he was hefted into a big chair, an IV drip put into his arm and strange glasses placed over his eyes.

A surge of chemicals rejuvenated him, and he stared at his metallic surroundings. "That was some Perfect Cube," he muttered, conscious of a bloody, bruised abrasion on his leg.

The rebels laughed. "That? That wasn't the Perfect Cube. Its dimensions weren't even exact. This is the Perfect Cube." A small cube, exact perfect dimensions of a couple inches on each side, was placed on a stand in front of Quaddy.

"What is it?"

"More like, who is it," someone said. "They are our leader. A visionary. The greatest mathemitician ever. The Perfect Cube."

A light glowed suddenly on the cube's face and shone into Quaddy's eyes. He squinted, feeling it probe into his mind.

Yes... yes... you should be easy to crack, mused a voice that was inside of his brain. It was an unsettling feeling, as if numerical tentacles were probing his mind.

"Wha - what do you want?" Quaddy stammered.

Solve the following sequences, the Perfect Cube demanded. Quaddy could feel himself eager to solve them. The thing was taking over his mind!

(1) Two strands, entangled together:

Ones Strand:	0-1-1-1-2-2-1-3-3-2-5-4-2-?

Zeroes Strand:  1-0-0-1-0-1-3-1-2-4-1-3-6-?

(2) Each part of the sequence contains multiple numbers:

[0/1] [1/0] [1/1] [2/0] [1/2] [1/1/1] [3/0] [1/3] [1/2/1] [1/1/3] [2/2] [?]

(3) The following sequences each follow the same rule to generate the next number:

12, 7, 7, 7, ...

16, 8, 6, 5, 5, 5, ...

70, 14, 9, 6, 5, 5, 5, ...

4, 4, 4, 4, 4, ...

100, 14, 9, 6, 5, 5, 5, ...

360, 17, 17, 17, ...

512, 18, 8, 6, 5, 5, 5, ...


What will follow the number 42, and why?

(4) What is next in the sequence?

138

777

795

1995

?

Quaddy gave the answers, gasping in pain.

Good, good the Perfect Cube hissed contentedly. I have raided your brain for all of the information we wanted earlier, and more. You are of no further use to us. Goodbye, Quadrangle.

Uh-oh.

Quaddy looked desperately to either side. Behind him, a door, guarded by rebels. In front, the vent to a mysterious vertical shaft...

What are the answers to the sequences? And how should Quaddy escape?

Edited November 20, 2008 by unreality

[Izzy]

It probably isn't, but is 1155 remotely close? Or 385?

Because...

138 = 2 * 3 * 23

777 = 3 * 7 * 37

795 = 3 * 5 * 53

1995 = 3 * 5 * 7 * 19

138 and 777 have interesting prime factorizations, and then 795 is that but backwards, but I'm lost on 1995.

[unreality]

0-1-1-1-2-2-1-3-3-2-5-4-2-? = 7.

If you add the first 2 bolds numbers you get the 3rd number.

Then start again with the result with the 2nd number from it ect...

Maybe wrong but atleast I figured out a pattern

This is for #1, right? You may be onto something - that would be an interesting property, although that's not the defining property of the sequence. That was just the Ones Strand, right? Here's a hint for #1

I call the entirety of Sequence #1 by this name: Fibonary ;D

If you're still struggling, this was solved by armcie a page or so back, see post 16 for details

It probably isn't, but is 1155 remotely close? Or 385?

Because...

138 = 2 * 3 * 23

777 = 3 * 7 * 37

795 = 3 * 5 * 53

1995 = 3 * 5 * 7 * 19

138 and 777 have interesting prime factorizations, and then 795 is that but backwards, but I'm lost on 1995.

I just realized a stupid mistake I made...... 1995 shouldn't be in the sequence at all!!! GAHHHH!!!! I'm an idiot, I'm so sorry!

Sequence for Number Four:

138

777

795

???

What is the next item in the sequence?

Also, anyone make any progress on #2?

[Izzy]

I think the next number is 1995? Or at least I know now how you got it... 5 * 7 * 57. But 57 isn't a prime number... so is that where you went wrong?

Making the next number 5 * 9 * 59 = 2655

I'm pretty sure that's right.

[unreality]

Nope

Spoiler for only Izzy should read this:

Spoiler for are you sure, Izzy?:

9 = 3 * 3

Edited November 23, 2008 by unreality

[Izzy]

>_> I knew that! Really! Man am I kicking myself.

3*7*73 = 1533

If that's wrong, am I at least on the right track?

[unreality]

#1 - armcie (see post 16)

#2 - UNSOLVED

#3 - Grayven (see post 16)

#4 - Izzy (see THIS post )

1533

Spoiler for explanation:

138

777

795

Break them down into their prime factors:

138 = 23 * 2 * 3

777 = 37 * 3 * 7

795 = 53 * 5 * 3

So the next number is:

1533 = 73 * 7 * 3

138 is the first possible number, and 1533 is the last possible number, if you are keeping the first number as two digits

Edited November 23, 2008 by unreality

[Izzy]

#4 - peace*out (see THIS post )

Dude, what?

[peace*out]

#1 - armcie (see post 16)

#2 - UNSOLVED

#3 - Grayven (see post 16)

#4 - peace*out (see THIS post )

1533

Spoiler for explanation:

138

777

795

Break them down into their prime factors:

138 = 23 * 2 * 3

777 = 37 * 3 * 7

795 = 53 * 5 * 3

So the next number is:

1533 = 73 * 7 * 3

138 is the first possible number, and 1533 is the last possible number, if you are keeping the first number as two digits

Dude, what?

Thanks, but i didn't do anything..

[unreality]

woops, I confused your names, sorry!! I edited it, it's all fixed now ;D Good job Izzy! #2 is the last one left

[Izzy]

Yeah, I got nothing for 2. I looked into Binary code and what the numbers meant and everything, but I can't solve it.

Unless this random somewhat pattern means anything.

]

0

Div by 0

1

Div by 0

1/2(10)

1

Div by 0

1/3(11)

1/(2)((10))

1/(1/3)

1

?

[unreality]

Yeah, I got nothing for 2. I looked into Binary code and what the numbers meant and everything, but I can't solve it.

Unless this random somewhat pattern means anything.

]

0

Div by 0

1

Div by 0

1/2(10)

1

Div by 0

1/3(11)

1/(2)((10))

1/(1/3)

1

?

Uhhh what is that?

lol

[unreality]

See my About Me page for a clue ;D If (during my temporary ban) I see someone gets the right answer, I could have someone else post whether or not you are correct

[Guest]

See my About Me page for a clue ;D If (during my temporary ban) I see someone gets the right answer, I could have someone else post whether or not you are correct

I think I'm close*...

[0/1] [1/0] [1/1] [2/0] [1/2] [1/1/1] [3/0] [1/3] [1/2/1] [1/1/3] [2/2]
0 1 1 10 11 101 1000 1101 10101 100010 110111 1011001

The second line is the binary representation of fibonacci again

The code seems to describe the binary in some way, although I'm not sure of all the rules.

[1/1/3]

means:

one digit, then one other digit, then three of the first digit (and then 1?)

010001

reversed gives us 100010

[3/0]

means

three zeros (and then 1) reversed

1000

[1/1/1]

means

one of one digit, one of another, then one of the first (reversed cos it makes no difference)

101

[1/2]

would seem to be two ones 11

[1/1]

would be one one 1

But... [1/0] = 1; [2/0] = 10 and [3/0] = 1000 Which ain't exactly consistant

and some of the others seem to have minimal connection...

.... so, either there's a mistake in the riddle (doubtful) There are some subtlties I'm not taking into consideration (possible) or I'm barking entirely up the wrong tree (probable)

Anyway... using my partial understanding of a set of plucked out of the air rules, I reckon the next entry in the code will be:

[1/2/2/1]

But even that doesn't tie in with the hint...

If anyone thinks this is worth taking any further, then one thing to bear in mind is that binary numbers always start with 1

*but having actually put this in writing, maybe not.

[unreality]

1s/0s/1s/0s/etc

binary numbers:

0 = [0/1]

1 = [1/0] < guess it should have been just [1], doesn't really matter

10 = [1/1]

11 = [2/0] < could have been just [2], again it doesn't really matter

100 = [1/2]

101 = [1/1/1]

1000 = [1/3]

1001 = [1/2/1]

1011 = [1/1/2]

1100 = [2/2]

the next number is 1101, which is [2/1/1]

[Guest]

1s/0s/1s/0s/etc

binary numbers:

0 = [0/1]

1 = [1/0] < guess it should have been just [1], doesn't really matter

10 = [1/1]

11 = [2/0] < could have been just [2], again it doesn't really matter

100 = [1/2]

101 = [1/1/1]

1000 = [1/3]

1001 = [1/2/1]

1011 = [1/1/2]

1100 = [2/2]

the next number is 1101, which is [2/1/1]

SHould have got that :S

[Guest]

1s/0s/1s/0s/etc

binary numbers:

0 = [0/1]

1 = [1/0] < guess it should have been just [1], doesn't really matter

10 = [1/1]

11 = [2/0] < could have been just [2], again it doesn't really matter

100 = [1/2]

101 = [1/1/1]

1000 = [1/3]

1001 = [1/2/1]

1011 = [1/1/2]

1100 = [2/2]

the next number is 1101, which is [2/1/1]

That's not even the same sequence! What happened to [3/0]???

Oh welcome back, by the way. We missed you

EDIT: wait a minute, [3/0] should be in there but preceded by [2/1]. Missed a couple of binary numbers there, that binary sequence is...

0,1,2,3,4,5,8,9,11,12

where's 10 gone? and "[1/1/3]"?

Oh I'm glad I didn't spend longer on that

[Guest]

...oh and I really think Quaddie needs to stay away from that mysterious shaft. Better to give the IV bag a squeeze for an extra boost of rejuvenation chemicals then fight his way out. IV stands are good for hitting people with, and the Perfect Cube could make a useful hostage (I wonder if the IV contains essence of Quaddy - is that intravenous or roman numerals?)

[unreality]

That's not even the same sequence!

Yeah the list I gave in my most recent post (the one that revealed the answer) wasn't comprehensive, I was just putting them down as they came to me... sorry if the actual OP list was incorrect.... woops

Oh welcome back, by the way. We missed you

Thanks ;D

sorry I screwed up #2... it was the thought that counted hehe. I thought it was a cool sequence, too bad I ruined it