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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 :P]

"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 by unreality
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he captures the PC (perfect cube), and threatends to smash it if they dont let him escape. If the PC takes over his mind, he trys to solve math puzzles, ignoring the words or the powerful PC...just a guess of course...

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"...What will follow the number 42, and why?..." - unreality

where is the # 42? (unless im a moron, i anyone can see it...)

He means for that part, what sequence would the number 42 create? I assume that section has the same sequence beginning with different numbers, but I'm lazy and not good at these so I'll let someone else do it.

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"...What will follow the number 42, and why?..." - unreality

where is the # 42? (unless im a moron, i anyone can see it...)

In the codebox where that question is, there is a variety of 'starting numbers' which are followed by sequences. I'm asking what sequence would follow 42

ie, the sequence starting from 100 is:

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

the question is, what is the sequence if you start with 42?

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"Look!" he shouted, pointing wildly. "An uncommon denominator!"

I've been paraphrased!... I'm flattered. :blush:

I'll leave the math to others until dust off my math skills a little more. As for the Quadsters next move? Bust out with some high powered Kung Four moves! It's about time those lessons paid off. Kick the cube off the stand into the chute and dive in after it! Ki-YA! (would you have prefered TriQuadDos?)

Very entertaining riddles, btw. I loved choose your own adventure books when I was young... so long ago.

edit: I only vote for the chute as long as there is no trash compactor at the bottom. I just won't do it. ;)

Edited by Grayven
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In the codebox where that question is, there is a variety of 'starting numbers' which are followed by sequences. I'm asking what sequence would follow 42

ie, the sequence starting from 100 is:

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

the question is, what is the sequence if you start with 42?

I was looking for the 42 myself.

These are good.

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1998? I will be shocked if it is, but I've got this strange feeling...

nope

:P sorry

12,7,7,7? Either I've gone loony, I'm completely wrong, or I'm actually getting my math back. Dare to dream!

42, 12, 7, 7, 7, ... is:

Spoiler for ???:

correct :D But why?

I'm probably way off, but whenever I see the numbers 1, 3, and 8 together, I think Fibonacci. Bonanova mentioned other modes and you having a love for them. Maybe that has something to do with the answer?

Fibonacci has something to do with one of them, but not #4 ;D

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armcie is right :D

Spoiler for answer:

I call this one Fibonary ;D The Fibonacci sequence in Binary is:

0,1,1,10,11,101,100,1101,10101,100010,110111,10010000

The Ones Strand is the number of Ones in each number, the Zeroes is the number of zeroes

The next Fibonary number is 11101001, so the Ones Strand is 5 and the Zeroes strand is 3 :D

Nobody has #2 yet, nor is remotely close :P

Grayven is correct:

42, 12, 7, 7, 7, ...

Spoiler for why:

break down the number into its prime factors, then add them together for 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, ...

It's interesting that the only way to end in a non-prime loop is starting with 4. However there's no way to get to 4 unless you start with a 4 :D

Nobody has squat on #4 :P

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