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Quaddy's mother's cooking was amazing, with all the right ingredients, so he had no problem hopping on his pentacycle the next day and heading back to the Numeraland Grocery Store. His mom had given him two separate grocery lists, and needed all the ingredients. This time, Quaddy knew better and looked at them beforehand:

First List: 0, 1, 1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, 91, 101, 103, ___

Second List: 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, ___

"That's a lot of ingredients," he mused, checking to make sure he had enough fractals to pay for it. "And both series are missing their last number! Both are smudged out! I'm beginning to think Mom does that on purpose to give me some mental exercise."

Still, Quaddy was an intelligent Numeralandian, and soon uncovered both of the final numbers. Happily, he started to pedal toward the Grocery Store. He was only in front of Poly Hedron's Jewelry Shop....

... when someone hit him like a runaway theorem!

"Ahhhh!" Quaddy yelled as his pentacycle spilled him onto the street. He struggled to get up but a heavy boot cracked sideways into his skull, and he collapsed to the street again, his vision hazy and Incomplete (Gödel was right). Weird numbers floated in his mind (70 and 836 were the first he saw) and he hardly noticed as his attackers (there was more than one) lifted him up and dragged him into some sort of vehicle. Then there was the sensation of moving (perhaps a cosine wave) that sent Quaddy drifting into unconsciousness.

When he woke, he was in an industrial warehouse of some sort. Yawning, he squinted open his eyes, conscious of the dried blood on his forehead. Probability tape (also known as Luck Tape, or even Duct Tape in some cultures) fastened his hands to a cold, hard metal chair. He kicked in an effort to move, but the chair was bolted rigorously to the floor.

"Awake, are you?" chuckled a voice, and Quaddy realized that a cyan-colored light had been emanating from a crack in the warehouse in front of him, but it was blocked now... by the silhouette of a tall, imposing man. "Do you know where we are?"

"Uh... a warehouse?"

"So ignorant," murmured the man, stepping closer. With surprise, Quaddy saw the logo of the Axiom Police on the man's shirt. What was law enforcement doing kidnapping people? "You are too young to understand, too young to remember."

"Remember what?"

Ignoring him, the man ranted on. "Too young to know, too young to see the truth! This, boy, is where numbers used to be made!" He finished his sentence with the air of sad wonder, as if looking through the past at a thing that was once beautiful but was now deformed and sick.

"There are many of us rebels," the officer explained. "Planted all over Numeraland, planning, waiting. One of the things we need is military codes." He seemed to remember Quaddy was there. "Your mother works for the Government, boy! She codes her messages in her grocery lists and sends them with you to the store, where her contact sees what you buy and sends the code on to the Government. What were you going to buy for her today???"

"What - uh - my mother - she - no!" Quaddy snapped. "What are you talking about? Let me go! Let me go! My mother's not an agent! She-"

"Then why does she blur out the last number in every series?" the Axiom Police rebel snarled, snatching away the grocery list from Quaddy's hand, which had just retrieved it from his pocket. The rebel pointed to the missing spaces. "In case you get captured, that's why! She relies on your intellect to fill in the missing piece at the store. So tell me... what are the last numbers of these series?"

The rebel showed Quaddy the list again:

First List: 0, 1, 1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, 91, 101, 103, ___

Second List: 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, ___

"Um... uh..." Quaddy knew what they were, of course. But what to say?

What are the missing numbers? And what should Quaddy tell the rebel? (It will determine future installments of the story :P)

[edit - grammar]

Edited by unreality
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The next numbers are 107 and 4.

The first sequence just adds all the previous digits: 103 + 1+0+3 = 107.

The second sequence belies UR's fascination with Fibonacci:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ...

which taken mod 5 becomes

0, 1, 1, 2, 3, 5, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, ....

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Good job :D

Yes the first series is the summation of all previous digits in the series

The second is the Fibonacci mod 5, as you pointed out - you could figure out the Fibonacci equivalent, then mod5 it, but it also works to use the previous two modded versions, ie, for the 8th and 13th, you didn't need to do (8+13) mod 5 = 1, you can do 3+3 mod 5 = 1 too. Anyway you nailed both of them (although you made a mistake in your listing at the very end, you said "5" in part where it was "0", it doens't matter but I thought I'd just point that out ;D).... but the second half remains un-answered - do you tell the truth... or lie? If so, what do you lie about? How do you lie? I'll take the general consensus of all of the answerers ;D

Edited by unreality
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The next numbers are 107 and 4.

The first sequence just adds all the previous digits: 103 + 1+0+3 = 107.

The second sequence belies UR's fascination with Fibonacci:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ...

which taken mod 5 becomes

0, 1, 1, 2, 3, 5, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, ....

Well...

for the second sequence, he should say... "well... the sequence goes variables a, 0, a, a, and then after repeating the first number in the sequence, b, 0, b, b, then another # in the sequence, and so it is 1."

in the next sequence, he says, "first you take the log of the first number, and then round it, and square it, and lastly, multiply it by 932, and you find the next number and factorial the first number, and add the first and shove it under the function f(x) = 4x+3!-408.588, and round that, then... LOOK! A REPEATING DECIMAL!" and take some interest to getting to the store.

I HAVE NO IDEA WHAT I JUST SAID, and hopefully, the Axiom police don't either.

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Well...

I HAVE NO IDEA WHAT I JUST SAID, and hopefully, the Axiom police don't either.

for the second sequence, he should say... "well... the sequence goes variables a, 0, a, a, and then after repeating the first number in the sequence, b, 0, b, b, then another # in the sequence, and so it is 1."

in the next sequence, he says, "first you take the log of the first number, and then round it, and square it, and lastly, multiply it by 932, and you find the next number and factorial the first number, and add the first and shove it under the function f(x) = 4x+3!-408.588, and round that, then... LOOK! A REPEATING DECIMAL!" and take some interest to getting to the store.

NAH! You simply tell the Axiom Police that you start with the last number of pi and work your way backwards.

That should keep them busy for a while!

Meanwhile, Quaddy would be thinking "If I got smart with you, how would you know?"

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