Google's "e" commerce

Last week, Google placed a billboard on highway 101 in the silicon valley (see picture to the right). It read:
{first 10-digit prime found in consecutive digits of e}.com

I was unaware of this until I saw a link on Jason Kottke's site on Monday. The link pointed to http://www.7427466391.com, which itself was the answer to the billboard puzzle. http://www.7427466391.com presented:

Congratulations. You've made it to level 2. Go to www.Linux.org and enter Bobsyouruncle as the login and the answer to this equation as the password.

f(1)= 7182818284
f(2)= 8182845904
f(3)= 8747135266
f(4)= 7427466391
f(5)= __________

I thought the f(1) result looked kind of familiar, so I looked at Pi, Phi, and then found it as the first 10 digits after the 2 in e (2.7182818284...)---then a quick find of "e to the 10,000 digit", and some grep'ing, showed that the other 10 digit sequences were in e too. They are the first 10, then 4 digits in, then 24 in, and finally 99 digits in (I think, I counted these by hand on a print out).

I sat there pondering what they had in common, what the f(x) might be, for several hours. Are they evenly spaced? nope. Are they like e +1/1 or something like that? I tried many simple algorithms, and nope. I didn't think it would be some crazy reverse engineering of a complicated algorithm, but with Google, I wasn't quite sure. Is this something that should be simple and take like 10 minutes to figure out (like the usually simple, but non-obvious questions on an IQ test), or is it some complex thing that they want only 20 people to have the knowledge and skill to figure out? After awhile, I was beginning to wonder, since the pattern wasn't coming to me.

So, I decided to try the tricky stuff.

First, I multiplied the digits, to see if each result had something in common. I thought this was pretty clever, but it didn't work. I tried some failed division of digits in each result. That just made me confused. Then I thought,"oh yes! I bet if you multiply each digit in each group together, you get the next one! nope. I bet if you subtract the first result from the second, you get the third! nope. I bet if you add the two results together, you get the next! Like the fibbonacci sequence! nope. Shit. Fine.Well, if you add the digits up in the first group, you get 49. Nice. Well, try the second one. HMMMMM.49. The third one...yeah! yeah! yeah! that rules!"

So, if you add the digits up, one by one, in each group, you get 49. Like, in the first group, you do this:
7+1+8+2+8+1+8+2+8+4 = 49

and the second one:
8+1+8+2+8+4+5+9+0+4 = 49

the same for the third and fourth ones.

Man, thats weird. And cool. And a pattern. And the answer.

Now, you gotta figure out the 5th one. What is f(5)?

So, you gotta find 10 digit groups, where each digit in the group, when added together, equals 49.

Oh yeah, I later found out, when my program was not outputting what I expected to see, that the 10 digit groups need to be consecutive.

Like, the first group is:7182818284
and then you have to slide your "10 digit group" over to the right in the results of e, like so:

| 7182818284 | 5904523536
7 | 1828182845 | 904523536
71 | 8281828459 | 04523536
718 | 2818284590 | 4523536
7182 | 8182845904 | 523536

each group between the pipes is the 10 digit group you have to check; to see if the individual digits add up to 49. If they do, you're cool. If they don't, you do the Mos Eisley stormtrooper, "move along, move along." Kinda like bitwise operations (where you move one's around in zeros to do binary arithmetic, like 00010 to 00001).

Blah. So anyway, I had to write some php to do this for me, as doing it by hand would cause God to kill a kitten.

Here is the php:

/*

take a txt file with the digits of e
start with the first to the tenth digit
check to see if it adds up to 49
if it does, display it
move to 2nd through the 11th digit
then the 3rd through the 12th digit
etc

*/

$e=file_get_contents('e.txt'); // 10,000 digits of e (or whatever) after the "2.", one string, no newlines

$e_length=strlen($e); // how many digits in e input

for( $r=0; $r<$e_length; $r++) {

$monkey[] .= substr($e,$r,10); // monkey is e string, r is start point (incremented each iteration), groups of 10 digits

}

foreach($monkey as $k){

$i=0; // set iterator to 0
$answer=0; // set answer to 0, later we check if it is equal to 49

while($i != 10){

$answer = $answer + $k{$i};

$i++;
}

if ($answer==49){
print $answer . "
"; // 10 digit, consecutive groups that equal 49
print $k . "
"; // the actual sequence of digits that equal 49
}

}

and, here is some of the output:

49
7182818284
49
8182845904
49
8747135266
49
7427466391
49
5966290435
49
2952605956
49
0753907774
49
0777449920
49
3069697720

The answer to f(5) is in there somewhere.

Then you go to linux.org, and in the login box, username=bobsyouruncle and password=mystery number in the above output.

Then, you get directed to: http://www.google.com/labjobs/index.html

That's it! Pretty damn cool if you ask me.

THEN

I come to find out that the Market Share Price of the Google IPO is set at:

$2,718,281,828

That should look familiar. How Rad is that?

KMA

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