Google Labs Aptitude Test

Tigers2B1

Just got a copy of the Google Labs Aptitude Test (GLAT) as an insert in a magazine I get. Seems as if Google is actively recruiting since this is the second advertisement they have run in this mag, which typically only accepts classified ads. They add that if you score high enough – they'll "be in touch." Anyone else get a copy of this??

arnie cohen

Yeah, I got this quiz in Physics Today. Wonder if they'll really respond if one does well on the quiz or it's just a ploy to get us to use Google more.

So what did you get for numbers 1 & 3.

chroot

Let's be careful here, folks. We don't condone cheating here.

- Warren

chroot

I'm also very interested to know if the test is included in any "common" periodicals like Scientific American, which are available at most newsstands. I'd love to get my hands on a copy.

- Warren

maryellen

Dr. Dobb's Journal (October 2004) included the Google Labs Aptitude Test (GLAT).

Here is the quote from the cover:

"How much aptitude do you have for the sort of mind-bending engineering problems encountered each day at Google Labs? Take the GLAT and find out. Simply answer all questions to the best of your abilities (cheaters will answer to the karma police), fold completed exam into attached enveleope and send to Google Labs. Score high enough and we'll be in touch. Good luck."

recon

I've received my September copy of the Scientific American. I did not see any Google Aptitude Test. Is the test available online?

Gokul43201

<searching frantically> Where's my Physics Today ?

phoenixthoth

Apparently google is posting billboards with this puzzle:
{first 10-digit prime found in consecutive digits of e}.com

Visit that page (without braces) and get a new puzzle.

You go through enough hoops and they ask for a resume.

I solved the first one and went to the website. The second puzzle seems to require more creativity over raw computational skill and the ability to program a computer. Or maybe there's a really ingenious way to solve this with pencil and paper. I'll just say that the next question is a sequence question; one that required more than 10 seconds of lateral thinking on my part. I haven't solved it yet. I would rather die than work for google but I'm finding these puzzles entertaining.

recon

I'm too young to work for Google. But I would like to know how to find the first 10-digit prime in consecutive digits of e. Is there a lot of mathematics involved in this, or is it just a brain teaser that non-mathematicians are able to solve?

Anyone care to let me in on the solution?

recon

I just read somewhere on the net that the billboard puzzle can only be cracked through brute-force.

phoenixthoth

Well I bet Ramanajuan could do it with pencil and paper but, yes, I used brute force for both problems. The second problem requires brute force as well as some ingenuity. I used mathematica which makes solving it really simple. It has commands that let you extract and play with the digits of e, a command for primality testing, and then reconstruction back into a number. The solution occurs around digit number 100 (I think) and testing 10 digit numbers for primality takes no time at all so this isn't the test of a master programmer. I expected the solution to come only after millions of digits; not because that's what I mathematically expected but because I expected it to be that hard. I expected it to require tricks and math theorems to make the brute force go faster but it just took about 9 seconds on my machine to run through and test. The second problem took about a minute on my machine.

TenaliRaman

i did that easy,
used google for the first and online integer sequence for the second
now will my resume be accepted , i dunno

-- AI

Gokul43201

Surely they can't object to your using Google !!

TenaliRaman

Prolly i should post that resume after all .....

Codemaster

RIDDLE ME THIS... TRIVIA QUESTION

(i made it pass all the trivia and sent in my resume to google for the job of coder)

WHAT IS THE ANSWER FOR {First 10-digit prime found in consecutive digits of e}.com

2.718281828459045235360287471352662497757247093699959574966
967627724076630353547594571382178525166427427466391932003059
921817413596629043572900334295260595630738132328627943490763
233829880753195251019011573834187930702154089149934884167509
244761460668082264800168477411853742345442437107539077744992
069551702761838606261331384583000752044933826560297606737113
200709328709127443747047230696977209310141692836819025515108
657463772111252389784425056953696770785449969967946864454905
987931636889230098793127736178215424999229576351482208269895
193668033182528869398496465105820939239829488793320362509443
117301238197068416140397019837679320683282376464804295311802
328782509819455815301756717361332069811250996181881593041690
351598888519345807273866738589422879228499892086805825749279
610484198444363463244968487560233624827041978623209002160990
235304369941849146314093431738143640546253152096183690888707
016768396424378140592714563549061303107208510383750510115747
704171898610687396965521267154688957035035402123407849819334
321068170121005627880235193033224745015853904730419957777093
503660416997329725088687696640355570716226844716256079882651
787134195124665201030592123667719432527867539855894489697096
409754591856956380236370162112047742722836489613422516445078
182442352948636372141740238893441247963574370263755294448337
998016125492278509257782562092622648326277933386566481627725
164019105900491644998289315056604725802778631864155195653244
258698294695930801915298721172556347546396447910145904090586
298496791287406870504895858671747985466775757320568128845920
541334053922000113786300945560688166740016984205580403363795
376452030402432256613527836951177883863874439662532249850654
995886234281899707733276171783928034946501434558897071942586
398772754710962953741521115136835062752602326484728703920764
310059584116612054529703023647254929666938115137322753645098
889031360205724817658511806303644281231496550704751025446501
172721155519486685080036853228183152196003735625279449515828
418829478761085263981395599006737648292244375287184624578036
192981971399147564488262603903381441823262515097482798777996
437308997038886778227138360577297882412561190717663946507063
304527954661855096666185664709711344474016070462621568071748
187784437143698821855967095910259686200235371858874856965220
005031173439207321139080329363447972735595527734907178379342
163701205005451326383544000186323991490705479778056697853358
048966906295119432473099587655236812859041383241160722602998
330535370876138939639177957454016137223618789365260538155841
587186925538606164779834025435128439612946035291332594279490
433729908573158029095863138268329147711639633709240031689458
636060645845925126994655724839186564209752685082307544254599
376917041977780085362730941710163434907696423722294352366125
572508814779223151974778060569672538017180776360346245927877
846585065605078084421152969752189087401966090665180351650179
250461950136658543663271254963990854914420001457476081930221
206602433009641270489439039717719518069908699860663658323227
870937650226014929101151717763594460202324930028040186772391
028809786660565118326004368850881715723866984224220102495055
188169480322100251542649463981287367765892768816359831247788
652014117411091360116499507662907794364600585194199856016264
790761532103872755712699251827568798930276176114616254935649
590379804583818232336861201624373656984670378585330527583333
793990752166069238053369887956513728559388349989470741618155
012539706464817194670834819721448889879067650379590366967249
499254527903372963616265897603949857674139735944102374432970
935547798262961459144293645142861715858733974679189757121195
618738578364475844842355558105002561149239151889309946342841
393608038309166281881150371528496705974162562823609216807515
017772538740256425347087908913729172282861151591568372524163
077225440633787593105982676094420326192428531701878177296023
541306067213604600038966109364709514141718577701418060644363



If we browse the value of number 'e', we found that the first 10-digit prime number within these decimals is '7427466391'(which is a prime number).

2.718281828459045235360287471352662497757247093699959574966
967627724076630353547594571382178525166427427466391

So we add this prime number into the address box: '7427466391.com', which contains more clues.

--------

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)= __________ (answer: 6819025515)

Enter '6819025515' into the password box.
Enter 'Bobsyouruncle' into the login box.

--------

THE ANSWER TO THE FIRST TRIVIA QUESTION IS: google.com (IP 216.239.53.184)
Congradulations you have made it to level 3

Please solve the next problem...

The next puzzle they offer is:

Solve this cryptic equation, realizing of course that values for M and E could be interchanged. No leading zeroes are allowed:
WWWDOT - GOOGLE = DOTCOM

There are several ways to solve this:

1. Find solution on the internet (using Google)
2. Find a web application solving this kind of problems
3. Solve the problem manually
4. Write the code solving this class of the problems (even if it takes much longer than any of above)

-----

For me, approach number 4 is the most natural. I immediately recognized this as another opportunity to exercise in Haskell programming.

The result is [('C',4),('D',5),('E',6),('G',1),('L',0),('M',3),('O',8),('T',9),('W',7)] and this time I decided to publish my source code (I am still learning Haskell, so it is far from perfect). I do not care about performance, I was more concerned with clarity of the code, so on my Powerbook G4 it takes around 22 second to find the answer. Also, it finds only first of possible solutions. It should trivial to modify the code to find all possible answers.

This source code answer is below
---------

{-

Solves class of puzzles where arithmetic formula is expressed as sum
of 2 words. For example:

SEND
+MORE
-----
MONEY

According to http://www.tkcs-collins.com/truman/a...ha_solve.shtml

There are two rules that must be followed for solutions:

* The leftmost letter can't be zero in any word.
* There must be a one-to-one mapping between letters and digits.
In other words, if you choose the digit 6 for the letter M, then all
of the M's in the puzzle must be 6 and no other letter can be a 6.

This program was inspired by Google Labs Aptitude Test (GLAT):

http://cruftbox.com/blog/archives/001031.html

The puzzle mentioned in the test:

GOOGLE
+DOTCOM
-------
WWWDOT

Have 2 solutions in base 10.
They are:

1. C=4 D=5 E=6 G=1 L=0 M=3 O=8 T=9 W=7
2. C=4 D=5 E=3 G=1 L=0 M=6 O=8 T=9 W=7

However for simplicity sake this code only finds first one:

[('C',4),('D',5),('E',6),('G',1),('L',0),('M',3),('O',8),('T',9),('W',7)]

This Haskell source compiles under GHC and Hugs.

(c)2004 Vadim Zaliva

-}

module Main (main) where

import IO
import Prelude
import Maybe
import List
import Data.FiniteMap

Data ---

base::Int
exp0::[String]
expS::String

base=10
exp0=["DOTCOM","GOOGLE"]
expS="WWWDOT"

Code ---

-- Character used to fill empty decimal positions. It will be always mapped to '0'.
fillChar:: Char
fillChar = ' '

main :: IO ()
main = do
hPutStrLn stdout (show (fmToList (delFromFM (fromMaybe emptyFM (solveA exp0 expS)) fillChar)))

spacePad:: Int -> String -> String
spacePad n s = if sl String -> Maybe (FiniteMap Char Int)
solveA [] _ = Nothing
solveA as cs = solveStep (map (reverse . (spacePad n)) as) (reverse (spacePad n cs)) 0
(unitFM fillChar 0)
(\m -> (all (valueNot0 m) as) &&
(not (hasDupValues (eltsFM (delFromFM m fillChar)))))
where
valueNot0 m s = (lookupWithDefaultFM m 1 (head s)) /= 0
n = max (length cs) (maximum (map length as))
hasDupValues m = mv /= (nub mv)
where
mv = sort m

solveStep :: [String] -> String -> Int -> (FiniteMap Char Int) ->
((FiniteMap Char Int) -> Bool) -> Maybe (FiniteMap Char Int)
solveStep _ [] r m v = if r==0 && (v m) then Just m else Nothing
solveStep a c r m v = if not (elemFM ch m) then
invBase (\x->solveStep a c r (addToFM m ch x) v)
else if (isJust fv) then
invBase (\x->solveStep a c r (addToFM m (fromMaybe '!' fv) x) v)
else if (rem s base) == (lookupWithDefaultFM m 0 ch) then
solveStep (map tail a) (tail c) (quot s base) m v
else Nothing
where
ch = head c
fv = findFreeVar a m
s = r + sum (map (\x -> lookupWithDefaultFM m 0 (head x)) a)

findFreeVar:: [String] -> (FiniteMap Char Int) -> (Maybe Char)
findFreeVar [] _ = Nothing
findFreeVar (x:xs) m = if elemFM n m then findFreeVar xs m else Just n
where
n = head x

invBase:: (Int -> Maybe x) -> Maybe x
invBase fn = invBaseStep 0 fn
where
invBaseStep b f = if b >= base then Nothing
else if (isNothing res) then invBaseStep (b+1) f
else res
where
res = f b

----- End

SPOILER: Again, small Haskell program helped me to find missing number 5966290435, which like previous ones have sum of digits 49 and could be found in sequence of digits of 'e'.



BONUS TRIVIA

What is the significance of 49?

Google is based in San Francisco, California.
(2400 E. Bayshore Mountain Parkway).
Its the hometown of the NFL's: San Francisco 49'ers.



IN CLOSING....IF YOU WANT TO BE AN ENGINEER FOR GOOGLE...YOU BETTER LOVE TO DO THIS KIND OF STUFF!

Gokul43201

Before 49 refered to the NFL team based in SFO, the people that took part in the California Gold Rush of 1849 were refered to as '49ers.

chroot

Well, Google is actually based in Mountain View (2400 E. Bayshore Pkway, Mountain View, CA).

Damn, if this is all they required for a serious resume submission I missed the ****ing boat big time. These are not hard questions. Hell, some of Gokul's treasure hunt was more difficult. I really should have gone and gotten a copy of the test while I had the chance. :pout:

- Warren