Google Placement Interview questions with answers and careers

Google Interview questions with answers

GLAT (Google Labs Aptitude Test)
1. Solve this cryptic equation, realizing of course that values for M and E could be interchanged. No leading zeros are allowed.
This can be solved through the systematic application of logic. For example, cannot be equal to 0, since . That would make , but , which is not possible.Here is a slow brute-force method of solution that takes a few minutes on a relatively fast machine:
This gives the two solutions
777589 – 188106 == 589483
777589 – 188103 == 589486
Here is another solution using Mathematica’s Reduce command:
A faster (but slightly more obscure) piece of code is the following:
Faster still using the same approach (and requiring ~300 MB of memory):
Even faster using the same approach (that does not exclude leading zeros in the solution, but that can easily be weeded out at the end):
Here is an independent solution method that uses branch-and-prune techniques:
And the winner for overall fastest
2. Which of the following expresses Google’s over-arching philosophy?
A) “I’m feeling lucky”
B) “Don’t be evil”
C) “Oh, I already fixed that”
D) “You should never be more than 50 feet from food”
E) All of the above
[This exercise is left to the reader.]
3. This space left intentionally blank. Please fill it with something that improves upon emptiness.
For nearly 10,000 images of mathematical functions, see The Wolfram Functions Site visualization gallery .
4. What is the coolest hack you’ve ever written?
While there is no “correct” answer, a nice hack for solving the first problem in the SIAM hundred-dollar, hundred-digit challenge can be achieved by converting the limit into the strongly divergent series:and then using Mathematica’s numerical function SequenceLimit to trivially get the correct answer (to six digits),
You must tweak parameters a bit or write your own sequence limit to get all 10 digits.
5. What number comes next in the sequence: 10, 9, 60, 90, 70, 66, ?
A) 96
B) 1000000000000000000000000000000000
C) Either of the above
D) None of the above
This can be looked up and found to be sequence A052196 in the On-Line Encyclopedia of Integer Sequences, which gives the largest positive integer whose English name has n letters. For example, the first few terms are ten, nine, sixty, ninety, seventy, sixty-six, ninety-six, ?. A more correct sequence might be ten, nine, sixty, googol, seventy, sixty-six, ninety-six, googolplex. And also note, incidentally, that the correct spelling of the mathematical term ”
googol” differs from the name of the company that made up this aptitude test.
6. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters?
(Assume that ABC is constructed so that a solution does exist.)
This is the isoperimetric point , which is at the center of the larger Soddy circle. It is related to Apollonius’ problem . The three tangent circles are easy to construct: The circle around has diameter , which gives the other two circles. A summary of compass and straightedge constructions for the outer Soddy circle can be found in ” Apollonius’ Problem: A Study of Solutions and Their Connections” by David Gisch and Jason M. Ribando
7. ‘Tis known in refined company, that choosing K things out of N can be done in ways as many as choosing N minus K from N: I pick K, you the remaining.
This simply states the binomial coefficient identity .
Find though a cooler bijection, where you show a knack uncanny, of making your choices contain all K of mine. Oh, for pedantry: let K be no more than half N.’Tis more problematic to disentangle semantic meaning precise from the this paragraph of verbiage peculiar.
1 1
2 1
1 2 1 1
1 1 1 2 2 1
What’s the next line?
312211. This is the “look and say” sequence in which each term after the first describes the previous term: one 1 (11); two 1s (21); one 2 and one 1 (1211); one 1, one 2, and two 1′s (111221); and so on. See the look and say sequence entry on MathWorld for a complete write-up and the algebraic form of a fascinating related quantity known as Conway’s constant.
9. What’s the next number in this sequence: 10, 9, 60, 90, 70, 66 … ?
A. Spell the numbers out:
They are in ascending order, based on the number of letters in the spelled-out numbers. A correct response will have nine letters: 96, for instance. A cleverer answer is “one googol.” That’s the huge number that can be written as a “1″ with a hundred zeros after it. Google, the company’s name, was
originally a misspelling of “googol.”
10. What will be the next great improvement in search technology?
Semantic searching of mathematical formulas. See for work currently underway at Wolfram Research that will be made available in the near future.
11. What’s broken with Unix?
Their reproductive capabilities.
How would you fix it?
[This exercise is left to the reader.]
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