a math riddle

[The Lady Shael]

After hours of fighting my way though dense jungle, I broke into a clearing.  A rickety bridge extended across the gaping, lava filled ravine.  I could see the hut containing the life-saving serum on the other side... I had to get across in the next few minutes, or die trying.



The entrance to the bridge was blocked by an enormous, roaring dragon... no hope of getting past it.



An ancient man sat cross-legged on the ground.  Next to him, extending off into the distance as far as the eye could see was a line of flat stones.  Some appeared black, and some white.



The old man was turning a pebble over and over in his hands; he looked up at me.  "If you solve the Riddle of the Stones, the dragon will fall asleep.  If you are wrong, the dragon will come over here and eat you."  He looked back down to his pebble.



Time was slipping away... I had no choice.



"Tell me the riddle then, old man, and I will solve it."



"Here it is", he said, rising slowly to his feet.  "Listen carefully.  I will recite it only once, and you may give only one answer."  He then told me this tale.



"In a past eternity, I  was a great mathematician who discovered the secret of infinity.  After wasting several eternities on frivolity, I decided to use them systematically.  During one, gathered the infinity of stones you see here.  Each stone is white on one side, and black on the other.  I first laid them out in this line, all white-side-up."



"I decided to use the next eternity adding some variety, so, I walked along the line and turned over every other stone, starting with the second.  An eternity later, the even numbered stones were all black-side-up, and the odd numbered stones were all white-side-up."



"This was a little too predictable for me, so, in the eternity after that, I walked along the line again and turned over every third stone, starting with the third.  This made stone 3 black-side-up, but now stone 6 (having been flipped twice) was white-side-up again, and so on, all the way down the line."



"In the next eternity, I turned over every fifth stone, starting with stone 5.  In the eternity after that, I turned over every seventh stone, starting with stone 7."



"Over the infinitely many eternities that followed, I carried out this process for the rest of the prime numbers:  11, 13, 17, 19, and so on... forever.  As you can see, some of the stones ended up white-side-up, and some black-side-up."



He paused, and took a deep breath.



"Since your time is running out, young man, I will now pose the Riddle of the Stones."



"Is stone number 1,000,000,000,000,000,000,000,000,000,000,000 white-side-up, or black-side-up?"



I thought for a few minute or two, then said confidently, ""It's obvious, sir.  It's _____-side-up".



The dragon immediately fell asleep.  I crossed the bridge, and was saved.



What's the answer? It's actually pretty simple if you're a math nerd. =) After enough people have guessed, I'll tell you the answer and why.

[Shade]

Psh. The solution is obvious.
...
...
...
Whack the old guy with something heavy and use him to lure the dragon away, while the dragons chows down, you run across the bridge   :)

[Shadow]

Black, because that huge number is not a multiple of a prime number, but it is an even number.

[Shade]

That would've been my second answer  ;)

[bjornredtail]

It is white. It was divisible by 2 and 5, but no prime number past that.

[wolf bite]

1,000,000,000,000,000,000,000,000,000,000,000 ...

... IS an even number.
... NOT divisible by 3
... IS divisible by 5
... NOT divisible by 7
... NOT a prime number

The stone was turned 2 times and now sits on white.


Wolf Bite

(makes post seeing that I was just beat to the punch)

[Shadow]

ahh i forgot about 5..  >:(

[The Lady Shael]

Yep yep, Nev and wolf are right. =)