Google's Math Puzzle 564
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."
Frustrating (Score:5, Interesting)
A hint for those who want it...
If you're searching through all of your number theory memories and reference texts for a solution, you've left the solution far behind.
Re:I'm a Reebok Sales Engineer! (Score:1, Interesting)
I'm a bit of a maths dunce but (Score:5, Interesting)
In case you're wondering -- or forgot -- e is the base of the natural system of logarithms, having a numerical value of about 2.71828 (though the number goes on forever).
Get file with copy of prime numbers. Get file with copy of largest precision of e. Use perl to scan for all 10 digit primes and then look for the first one in e.
Profit
or am I missing something?
Interesting (Score:5, Interesting)
E A S Y (Score:5, Interesting)
Use Google to find the solution to Google's puzzle. [google.com]
Guess they just want people who know how to use a search engine. :)
Re:not that complicated (Score:3, Interesting)
Re:The Answer (Score:5, Interesting)
Anyway, I guess I wasn't paying that close of attention during the IPO thing -
From the Wikipedia article: "In the IPO filing for Google, Inc., in 2004, rather than a typical round-number amount of money, the company announced its intention to raise $2,718,281,828, which is, of course, e billion dollars to the nearest integer."
Why? (Score:3, Interesting)
I suspect these are just ways around the legal prohibitions on testing job candidates. Employers want to identify the smartest job applicants, and these informal riddles allow them to do that legally.
Re:I'm a bit of a maths dunce but (Score:1, Interesting)
The Answer (Score:2, Interesting)
The digits are 7427466391.
Here is the website [7427466391.com] which has another puzzle, and it says :
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)= __________
The answer here is 5966290435. This number can also be found in the sequence of 'e'
this is old news - and... (Score:3, Interesting)
Re:not that complicated (Score:5, Interesting)
This one is actually quite easy. We look for a particular host name in Google's address space. So let's try:
Hmm, no luck. What about the /16?
Well, we have a candidate, and it is indeed the correct one.
Once you have that domain name, you can search for more information [google.com].
Re:Just Google for the answer! (Score:4, Interesting)
> search engine.
You never had to "know" anything, it's just that it was easier/cheaper/quicker to know something, or employ someone who knew, than it was to look it up. This is increasingly no longer true.
Re:Frustrating (Score:3, Interesting)
Google GLAT ( Google Labs Aptitude Test ) (Score:5, Interesting)
A few sample questions from it:
#2 Write a haiku describing possible methods for predicting search traffic seasonality.
#4 You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling about. What dost thou do?
A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.
B) Use the laptop as a digging device to tunnel to the next level.
C) Play MPoRPG until the battery dies along with your hopes.
D) Use the computer to map the nodes of the maze and discover an exit path.
E) Email your resume to Google, tell the lead gnome you quit and find yourself in a whole different world.
#9 This space left intentionally blank. Please fill it with something that improves upon emptiness.
#17 Consider a function which, for a given whole number n, returns the number of ones required when writing out all numbers between 0 and n. For example, f(13)=6. Notice that f(1)=1. What is the next largest n such that f(n)=n?
#20 What number comes next in the sequence: 10, 9, 60, 90, 70, 66, ?
A) 96
B) 1 followed by 100 zeros ( a Googol )
C) Either of the above
D) None of the above
#21 In 29 words or fewer, describe what you would strive to accomplish if you worked at Google Labs.
Re:Interesting (Score:1, Interesting)
Needless to say they couldn't even bother to have a machine acknowledge my existence when I sent my resume in.
Re:I wonder (Score:3, Interesting)
The second puzzle, at that site, is really stumping me. If there is indeed a third, I don't stand a chance.
Re:not that complicated (Score:3, Interesting)
Schools (Score:3, Interesting)
- Babson College [babson.edu] Wellesley
- Bentley College [bentley.edu] Waltham
- Berklee College of Music [berklee.edu] Boston
- Boston Architectural Center [the-bac.edu] Boston
- Boston College [slashdot.org] Newton
- Boston Conservatory, The [bostonconservatory.edu] Boston
- Boston University [bu.edu] Boston
- Brandeis University [brandeis.edu] Waltham
- Bunker Hill Community College [mass.edu] Boston
- Cambridge College [cambridge.edu] Cambridge
- Emerson College [emerson.edu] Boston
- Emmanuel College [emmanuel.edu] Boston
- Fisher College [fisher.edu] Boston
- Harvard University [harvard.edu] Cambridge
- Hellenic College [hchc.edu] Brookline
- Lesley College [lesley.edu] Cambridge
- MIT [mit.edu] Cambridge
- Massachusetts College of Art [massart.edu] Boston
- Massachusetts College of Pharmacy [mcp.edu]
- Mount Ida College [mountida.edu] Newton
- New England Conservatory of Music [newengland...vatory.edu] Boston
- New England School of Law [nesl.edu] Boston
- Northeastern University [northeastern.edu] Boston
- Pine Manor College [slashdot.org] Chestnut Hill
- Radcliffe College [radcliffe.edu] Cambridge
- Simmons College [simmons.edu] Boston
- Suffolk University [suffolk.edu] Boston
- Tufts University [tufts.edu] Medford
- Wellesley College [wellesley.edu] Wellesley
- Wentworth Institute of Technology [wit.edu] Boston
- Wheelock College [wheelock.edu] Boston
Of course the local hi-tech/biotech/medical/finance/insurance/governmand Allied Health Sciences Boston
Re:Google will ultimately fail . . . (Score:1, Interesting)
After all the whole purpose of Google is to transform language knowledge to a form understandable to computers, and the areas of language that cannot be reached by equations cannot be reached by a computer program such as Google, and thus they are essentially irrelevant to Google.
Communicating with Math (Score:4, Interesting)
Re:I'm a Reebok Sales Engineer! (Score:4, Interesting)
On a side note, someone was very clever over at Cingular.com [cingular.com]. The URL 8675309.com [8675309.com] redirects you to Cingular's web site. I'm sure that only a small percentage of people have tried that URL but I'm sure that means that hundreds or thousands of people were redirected.
Someone was definitely thinking when they set that up.
Re:Why? (Score:3, Interesting)
It is illegal to give job candidates intelligence tests. So if you want smart employees, you need to find a way around the law.
Legally, the determination of whether you are engaged in discrimitory hiring practices is not based only on your intent. It also includes discrepant impact; If any any test which you administer as part of you job selection process favors a particlar race, then you are guilty of discrimimation. Courts have ruled that tests which measure intelligence are an illegal test for purposes selecting job candidates.
The only exception is that if you can show that that the test specifically measures the skill required for the job. For example, you could give driving tests to drivers. I doubt that if these same math riddles were posed on a written exam that they would pass that legal test for job-relatedness. Google would have to show in court that searching for prime numbers was part of the work that these employees would be expected to do on the job. They ony way employers can get away with this is to pose the same questions informally.
Re:not that complicated (Score:3, Interesting)
What I want to know is the point behind that other billboard on 101, the one that says "Applications extreme makeovers TENFOLD HOTTER THAN HELL" and has a picture of a hairy pig wearing sunglasses and a scarf. I was guessing it was associated with the digits-of-e billboard, because both so completely fail to communicate anything useful to the passing motorist.
Re:not that complicated (Score:1, Interesting)
a: they're not
b: you could type it
c: it's an email address
Re:not that complicated (Score:2, Interesting)
Re:aaah (Score:1, Interesting)
Re:not that complicated (Score:5, Interesting)
A physics teacher gives each student a barometer, and tells them that using only the barometer and brief visits to the town's tallest building, they have to determine the height of the building. Grades would be awarded based on the most creative solution.
One student started at the top, took a reading, moved to the ground floor, took a reading, and then based on that information and the barometric pressure that day, determined the approximate height of the building.
Other students basically copied the first, although with different variations (bottom to top, etc)
The student who received the only A? He went to the basement. Found the building engineer's office. Knocked on the door. Told the guy who answered, "I have a fine barometer. If you tell me exactly how tall this building is, it's yours."
Re:not that complicated (Score:5, Interesting)
there is no function to it.
The variable in f(x) as f(1), f(2) is the x position of a ten digit number that sums to be 49.
With a tiny perl program it turns to be: 5966290435
This is in position 128 in the exp(1) number.
Re:Google GLAT ( Google Labs Aptitude Test ) (Score:2, Interesting)
1111111110 == 1111111110
which is floor((10^10/9) - 1).
Note that since 500,000,001 worked, and 1 works and 500,000,000 has no 1's in it, then any working values from 0-499,999,999 will repeat with 500,000,000 added. After that, the one above is the only one through 2 billion (where I stopped looking).
Re:not that complicated (Score:4, Interesting)
I'm curious what sort of person can do this
I'm not the original poster but I did solve the puzzles this afternoon without "cheating". I'm a psychology/philosophy major that hasn't seen a math book in 10 years and I was able to figure it out. What I find interesting is that the answer to the first question (at least how I solved it) was an indirect hint at how to solve the second puzzle. Good luck, it was fun to work through it.
Re:not that complicated (Score:5, Interesting)
Sir Ernest Rutherford, President of the Royal Academy, and recipient of the Nobel Prize in Physics, related the following story:
Some time ago I received a call from a colleague. He was about to give a student a zero for his answer to a physics question, while the student claimed a perfect score. The instructor and the student agreed to an impartial arbiter, and I was selected.
I read the examination question: "Show how it is possible to determine the height of a tall building with the aid of a barometer."
The student had answered: "Take the barometer to the top of the building, attach a long rope to it, lower it to the street, and then bring it up, measuring the length of the rope. The length of the rope is the height of the building."
The student really had a strong case for full credit since he had really answered the question completely and correctly! On the other hand, if full credit were given, it could well contribute to a high grade in his physics course and certify competence in physics, but the answer did not confirm this.
I suggested that the student have another try. I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he hadn't written anything. I asked if he wished to give up, but he said he had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please go on in the next minute, he dashed off his answer, which read:
"Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula x=0.5*a*t^2, calculate the height of the building."
At this point, I asked my colleague if he would give up. He conceded, and gave the student almost full credit. While leaving my colleague's office, I recalled that the student had said that he had other answers to the problem, so I asked him what they were.
"Well," said the student, "there are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of simple proportion, determine the height of the building."
"Fine," I said, "and others?"
"Yes," said the student, "there is a very basic measurement method you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units. A very direct method."
"Of course. If you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of g [gravity] at the street level and at the top of the building. From the difference between the two values of g, the height of the building, in principle, can be calculated."
"On this same tack, you could take the barometer to the top of the building, attach a long rope to it, lower it to just above the street, and then swing it as a pendulum. You could then calculate the height of the building by the period of the precession."
"Finally," he concluded, "there are many other ways of solving the problem. Probably the best," he said, "is to take the barometer to the basement and knock on the superintendent's door. When the superintendent answers, you speak to him as follows: 'Mr. Superintendent, here is a fine barometer. If you will tell me the height of the building, I will give you this barometer.'"
At this point, I asked the student if he really did not know the c
The Google billboard on US Highway 101 in CA (Score:3, Interesting)
Note that surface of the Sun is usually estimated to be about 5780K which is similar to the midpoint of the hell temperature range (5531.15K).
Therefore one might conclude that these "extreme makeovers" might be brilliant ...
thus the
need for sun glasses. :-)
I'm sure other interpretations exist.
Re:aaah (Score:3, Interesting)
On the other hand, did Google ever claim that this was a math problem? It is a problem, sure, but it is obviously not a request for a proof of Goldbach's conjecture. Jerf critiques the problem as "sophomoric" but I think that Jerf's complaint is "beating up a strawman" --- he claims that Google posed a math problem and then declares the problem stupid. It is a stupid math problem
And, after all, there is a specific set of correct answers, which are perfectly apparent to those who solve the suggested problems --- because they lead to recognition by somebody, perhaps Google --- of particular, quite reasonable answers. If you type in random responses, you're just incredibly unlikely to stumble into the "honeypot."
So (blush, gloat) I have to admit enjoying 45 minutes in the solution of the problems, when I should have been doing what I'm actually supposed to be doing. If only for providing me with 45 minutes of fun, I'm grateful for the problem --- math problem or no.
The quasi-mathematical nature of the problems requires one to either "cheat" by invoking search engines (which, as some have pointed out, may be a perfectly valid solution method as far as Google is concerned), or to demonstrate familiarity with computer tools that facilitate the discovery of the answers.
The very first problem is quite well posed, and if you can figure out how to generate the ten digit numbers, you don't have to look very far. A subsequent problem is very ill-posed (as jerf points out), but nevertheless a "human" is capable of inferring a kind of pattern with far less information than a "mathematician" would consider acceptable. Surely this is precisely the sort of thing that we hope search engines will do for us.
It was fun. Probably Google isn't going to offer me a job, but I had fun. Is that so bad?