Google's Math Puzzle

An anonymous reader writes "Commuters in Cambridge, Mass., are scratching their heads over signs challenging passers-by to solve a complicated math problem. The mysterious banners are actually a job-recruiting pitch from Google."

not that complicated

[CommanderTaco]

about 20 mins worth of programming, and i'm not that smart. it ends up taking you to this page [google.com].

More details on Google's Blog

[GillBates0]

Accessible in their 07/01 archives [google.com]

Monday, July 12, 2004 Warning: We Brake For Number Theory
If any Silicon Valley drivers have found that traffic is moving more slowly than usual these days on the southbound 101 right around Ralston, you may have us to blame. Last week we unveiled a billboard that's a bit unusual in that it promotes Google only to one very narrow constituency: engineers who are geeky enough to be annoyed at the very existence of a math problem they haven't solved, and smart enough to rectify the situation.

Google Billboard

In other words, the billboard (which offers problem-solvers the URL to, sorry, a page containing an even harder problem), is a recruiting campaign. We've always worked hard to hire the smartest engineers we can find, and we thought this would be a cool way to find a few more. Perhaps including you. If you're a math or computer whiz who doesn't happen to live within shouting distance of Palo Alto -- good luck, and we're looking forward to hearing from you.

- A. Googler

Been done before.

[rritterson]

This is at least the second time google has done this. The first was on a billboard along US 101 in Silicon valley. /. may have covered it then, but I can't find the article so here is one from news.com [com.com] (note that the caption to the picture if you read the NPR article also references the same billboard.)

This was posted before...

[Anonymous Coward]

I don't have the Slashdot link, but here's the linked-to article the last time around: (beware of Slashdot induced spaces in the url).

http://news.com.com/Google+recruits+eggheads+wit h+ mystery+billboard/2100-1023_3-5263941.html?tag=nef d.pop 2004-07-13 10:33:02
In a kind of geek "Jeopardy," the billboard read:"{first 10-digit prime found in consecutive digits e}.com." The answer, 7427466391.com, would lead a puzzle-sleuth to a Web page with yet another equation to solve, with still no sign the game was hosted by Google.

Mastering that equation would lead someone to a page on Google Labs, the company's research and development department, which reads: "One thing we learned while building Google is that it's easier to find what you're looking for if it comes looking for you. What we're looking for are the best engineers in the world. And here you are.

"As you can imagine, we get many, many resumes every day, so we developed this little process to increase the signal-to-noise ratio."

Re:More details on Google's Blog

[Maagma]

Direct Blog Post [google.com] [google.com] link to Google's hiring campaign market thingy. Ya.

I'm a Cheater

[Smuj]

I'm lazy, so I just Googled the answer [mkaz.com].

SPOILERS..

[doowy]

I actually don't want to spoil it, and nobody else should because it is a fun excersise..

I won't post the URL, but here's what it says in case you want a jump on the second question;

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)= __________

Unfortunatley, the fun ends here. When you enter the correct password, you are taken to google lab's hiring page which I presume is accessible without jumping through hoops.

Spoiler.........

[orion41us]

Answer to 2nd puzzle is @ http://www.mkaz.com/math/google/ [mkaz.com].......

All the solutions - spoilers

[Anonymous Coward]

All the solutions you need [mkaz.com]

Enjoy.

Picture of Google Billboard

[$exyNerdie]

Here's the Google Billboard picture [mattwalsh.com]

(Also note the ClearChannel name at the bottom of the billboard...)

The Answer...

[Paulrothrock]

Can be found out using a relatively short Perl script and some math knowledge.

First, find the first 1, 3, 7, or 9 after the first ten digits after the decimal. Take the preceding 9 digits, and run it through a Prime Number Checker. [uiuc.edu] (The algorithm is in the source).

Really, the hardest part is determining the farthest decimal points of e. Here's the formula: limn->infinity (1 + 1/n)n.

It's lazy, impatient, and full of hubris! BTW, I get a finder's fee.

Google's joke

[$exyNerdie]

This is a joke. Here's why:

Once you solve the billboard puzzle, you get to this page:
http://www.7427466391.com [7427466391.com]
that has the following text:

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)= __________

NEXT:
You go to http://www.linux.org and enter Bobsyouruncle as the Login name and enter 6969696969 as the password. You get this page:

LOGIN FAILED
Your attempt to login failed for the following reason:
we did not find a matching login/password.

Please Note:
For security reasons, your account will be locked after three login failures. If you have some doubt as to your login name or password, we suggest you go to the account problems page and have your password and/or login mailed to you while your account is still active.
Due to heavy administrative workload, locked accounts may take up to one week to be unlocked.


NEXT:
But if you want to skip that step, you can, because eventual goal is to get you to this web page:
http://www.google.com/labjobs/index.html [google.com]

Re:not that complicated

[meringuoid]

Interestingly, that's not cheating. That's exactly what Google are probably looking for. You didn't go charging through millions of digits of 'e' to find the answer; instead, you went looking for any long numerical URLs registered by Google.

That's a much more efficient search strategy. Just what they're after, methinks.

It's on Wikipedia since a while...

[flibuste]

You can find the answer on Wikipedia - The Exponential [wikipedia.org]

And it leads to: [7427466391.com]

However, I found it a nice challenge to take (not too complicated either), and if you get challenged that while working at Google, it must be a pretty interesting job to have.

Re:Dangerous?

[Flaming_cows]

Actually it is "...10 types of people..." as the first digit represents the 'ones'. 1 is just 1 and 10 is 2. Please learn binary before correcting people on it.

One-liner Mathematica solution to billboard puzzle

[coult]

I wrote this in a few minutes in Mathematica, and found the answer to the first puzzle. The second puzzle was annoying so I just searched google for it instead.

en = N[\[ExponentialE], 1000]; Table[x = (Floor[en*(10^k)*10^10] - Floor[en*(
10^k)]*10^10); If[PrimeQ[x], {k, x}, {k, 0}], {k, 0, 100}]

Solution

[simgod]

SPOILER

The solutions are:
http://www.7427466391.com/
and:
5966290435

Re:aaah

[BillyBlaze]

He's wrong anyway. Just because any number is a possibility doesn't mean it's the one they're looking for. You have to find a pattern. In this case, the pattern is f(n) = the nth 10-digit block of the digits of e whose digits add up to 49. f(5) is 5966290435. The linux.org login no longer works. And of course, I figured all that out with Google [google.com].

Re:I'm a bit of a maths dunce but

[Chatterton]

For your reference :)
The fisrt 10 000 digits :P

2.7182818284590452353602874713526624977572470936 99 95957496696762772407663035354759457138217852516642 74274663919320030599218174135966290435729003342952 60595630738132328627943490763233829880753195251019 01157383418793070215408914993488416750924476146066 80822648001684774118537423454424371075390777449920 69551702761838606261331384583000752044933826560297 60673711320070932870912744374704723069697720931014 16928368190255151086574637721112523897844250569536 96770785449969967946864454905987931636889230098793 12773617821542499922957635148220826989519366803318 25288693984964651058209392398294887933203625094431 17301238197068416140397019837679320683282376464804 29531180232878250981945581530175671736133206981125 09961818815930416903515988885193458072738667385894 22879228499892086805825749279610484198444363463244 96848756023362482704197862320900216099023530436994 18491463140934317381436405462531520961836908887070 16768396424378140592714563549061303107208510383750 51011574770417189861068739696552126715468895703503 54021234078498193343210681701210056278802351930332 24745015853904730419957777093503660416997329725088 68769664035557071622684471625607988265178713419512 46652010305921236677194325278675398558944896970964 09754591856956380236370162112047742722836489613422 51644507818244235294863637214174023889344124796357 43702637552944483379980161254922785092577825620926 22648326277933386566481627725164019105900491644998 28931505660472580277863186415519565324425869829469 59308019152987211725563475463964479101459040905862 98496791287406870504895858671747985466775757320568 12884592054133405392200011378630094556068816674001 69842055804033637953764520304024322566135278369511 77883863874439662532249850654995886234281899707733 27617178392803494650143455889707194258639877275471 09629537415211151368350627526023264847287039207643 10059584116612054529703023647254929666938115137322 75364509888903136020572481765851180630364428123149 65507047510254465011727211555194866850800368532281 83152196003735625279449515828418829478761085263981 39559900673764829224437528718462457803619298197139 91475644882626039033814418232625150974827987779964 37308997038886778227138360577297882412561190717663 94650706330452795466185509666618566470971134447401 60704626215680717481877844371436988218559670959102 59686200235371858874856965220005031173439207321139 08032936344797273559552773490717837934216370120500 54513263835440001863239914907054797780566978533580 48966906295119432473099587655236812859041383241160 72260299833053537087613893963917795745401613722361 87893652605381558415871869255386061647798340254351 28439612946035291332594279490433729908573158029095 86313826832914771163963370924003168945863606064584 59251269946557248391865642097526850823075442545993 76917041977780085362730941710163434907696423722294 35236612557250881477922315197477806056967253801718 07763603462459278778465850656050780844211529697521 8908740196

Re:Dangerous?

[AndrewHowe]

Well, I'm a programmer, and while I start ordinal numbering from 0, I start cardinal numbering from 1... Like everyone else. What's the declaration of the typesOfPeople array? How many elements are in it? 2. Or 10 in binary. How many elements are there in your empty set? -1?

I used Google to find the answer...

[foistboinder]

Math : Google Labs Problems [mkaz.com]

When do I start?

Re:not that complicated

[Florian Weimer]

Nice idea, except if you've only seen the billboard, how do you know it has anything to do with Google?

Good point, but the Google hint just makes it possible to use a more selective index. It's not required, strictly speaking.

If you haven't got this piece of information, you run into another problem: false solutions. In turns out that there is more than one ten-digit domain.

For example, how would you know that this site [2147483647.com] is the wrong one?

Re:not that complicated

[JPDeckers]

5966290435

Re:not that complicated

[parkrrrr]

You google for "digits of e" and select the second result [nasa.gov].

Re:not that complicated

[[e-mail]]

Because 2147483647 is the square of 46341.

No it's not. Squares can only end in 0, 1, 4, 5, 6 or 9.

Re:I'm a Reebok Sales Engineer!

[jrockway]

try http://www.7427466391.com/

Bobsyouruncle Password

[Anonymous Coward]

The password at www.Linux.org is 5966290435.

A crafty engineery already jumped through these hoops:
http://wernerkai.sites.uol.com.br/google/google.ht m [uol.com.br]

Re:Google GLAT ( Google Labs Aptitude Test )

[sgasch]

For #17 first I thought "it will never happen again". Then I thought "if I was really smart I'd prove this mathematically". Then I thought "I can write a 4 line C program to see..." Turns out I was wrong. If you're curious:

1 == 1
199981 == 199981
199982 == 199982
199983 == 199983
199984 == 199984
199985 == 199985
199986 == 199986
199987 == 199987
199988 == 199988
199989 == 199989
199990 == 199990
200000 == 200000
200001 == 200001
1599981 == 1599981
1599982 == 1599982
1599983 == 1599983
1599984 == 1599984
1599985 == 1599985
1599986 == 1599986
1599987 == 1599987
1599988 == 1599988
1599989 == 1599989
1599990 == 1599990
2600000 == 2600000
2600001 == 2600001
13199998 == 13199998
35000000 == 35000000
35000001 == 35000001
35199981 == 35199981
35199982 == 35199982
35199983 == 35199983
35199984 == 35199984
35199985 == 35199985
35199986 == 35199986
35199987 == 35199987
35199988 == 35199988
35199989 == 35199989
35199990 == 35199990
35200000 == 35200000
35200001 == 35200001
117463825 == 117463825
500000000 == 500000000
500000001 == 500000001
500199981 == 500199981
500199982 == 500199982
500199983 == 500199983
500199984 == 500199984
500199985 == 500199985
500199986 == 500199986
500199987 == 500199987
500199988 == 500199988
500199989 == 500199989
500199990 == 500199990
500200000 == 500200000
500200001 == 500200001
501599981 == 501599981
501599982 == 501599982
501599983 == 501599983
501599984 == 501599984
501599985 == 501599985
501599986 == 501599986
501599987 == 501599987
501599988 == 501599988
501599989 == 501599989
501599990 == 501599990
502600000 == 502600000
502600001 == 502600001

San Jose?

[DonGar]

They did this in San Jose a few months ago going North and South on 101. I just assumed it had hit slashdot then and I'd missed the article.

I saw the billboard and decided to solve it. Went googling for a list of pre-computed primes and found the answer already solved instead.