
Classic math puzzles for job interviews - pc
http://www.scribd.com/vacuum?url=http://pdos.csail.mit.edu/~petar/mathjob.pdf
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Tichy
I don't see how the square could be partitioned, maybe I am reading it wrong?
My informal counter proof by contradiction (decrypt with rot13.com):

fvapr gur cnegvgvba vf svavgr, gurer vf n fdhner Z jvgu gur fubegrfg fvqr. Abj
pbafvqre gur fdhnerf nybat gur gbc fvqr bs gur havg fdhner. Gur fznyyrfg
fdhner nzbat gurz unf n fvqr yratgu < 0.5, yrg'f pnyy vg F1. Abj pbafvqre ebj
bs fdhnerf pbirevat gur obggbz fvqr bs F1. Gurer unf gb or n fznyyrfg fdhner
nzbat gurz, jvgu yratgu < 0.5* fvqr_yratgu_bs(F1) = 0.25. Yrg gung fznyyrfg
fdhner or F2. Abj pbafvqre gur ebj bs fdhnerf ng gur obggbz bs gung fdhner.
Gurer unf gb or n fznyyrfg fdhner F3 nzbat gurz jvgu fvqr yratgu < 0.5*0.25 =
cbjre(0.5,3). Naq fb ba - gurer vf nyjnlf n arkg ebj bs fdhnerf, nf gur
fznyyrf fdhner va gur ebj pna abg gbhpu gur obggbz fvqr bs gur havg fdhner.
Urapr V pna tb ba yvxr gung vasvavgryl, orpnhfr yvz cbj(0.5,a) = 0 riraghnyyl
V'yy svaq n fdhner gung vf fznyyre guna Z, pbagenqvpgvba.

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kurtosis
These problems are a lot of fun and in most cases there are interesting
general lessons in their solutions, but the way the interview system seems to
work is that every year there's a new book or sheet of puzzles that everyone
memorizes and then pretends to have never seen before when asked during an
interview.

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bayleo
Yeah, these puzzles are too unique and are in many cases well known
problems/paradoxes that candidates are likely to know. Interviewers might be
better served by asking a generic, LSAT-style logic game or a somewhat simple
but time consuming math problem (maybe polynomial factorization).

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paulgb
#5 is impossible. Martin Gardner has a nice proof of this: observe that each
domino must cover a black and a white square, no matter how you orient it.
When you remove two opposite squares, you remove two squares of the same
colour. Imagine you have put 30 of the dominoes on the board, then two squares
remain uncovered. These squares must be the same colour (by the above rules),
so there is no way the last domino can cover them both.

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Zeromus
Ok, I fail and don't get the job, I get it... but where are the answers!

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billroberts
In what kind of job interview would asking any of these help you select an
employee?

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nickb
Professional puzzle solver job interview!

In all seriousness, if you start getting these questions during the interview,
you should realize that these people don't know how to hire and you should
move away.

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jatemack
Need answers? Email the PDF creator.

"Due to popular demand: I will write up and give out the solution to any
problem in return for an interesting new problem. This will serve as a good
growing force for the collection of problems."

<http://pdos.csail.mit.edu/~petar/misc.html>

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abossy
Wow, I am surprised #13 is listed as a 1-star problem.

I was told a story about this problem by a professor while in class.
Supposedly, Edgser Djisktra couldn't sleep one night due to jet lag. He was
currently going through a phase in which was exercising the power of thought,
practicing thought-exercises such as these without a pencil and paper. While
in bed that night, awake due to jet lag, he solved this problem. The professor
told us that none of us were smart enough to solve this problem. Hardly seems
worthy of one star. :)

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Tichy
I haven't solved it yet, but it seems to be solvable by sheer diligence? Is
there a faster solution? I think in an interview I would ask to write a
computer program that solves it. Wait - I guess now I have to try that :-(

Edit: which programming language has good support for primes? I thought I saw
one recently, but can't find it now.

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ChaitanyaSai
Using the Goldbach Conjecture makes it easier.

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Spyckie
start small and work your way up?

lets say 1>x>y and x+y<=4...

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redorb
on the mouse one, could you not mix wines?

100 bottles, divide into 2 groups, feed mouse...

Separate poisoned bottles into 2 groups feed mouse..

basically 100,50,25,12,6,3,1 ... 6 mice needed.

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martianpenguin
There is only 1 day. Wouldn't you just separate the bottles evenly across all
the mice?

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paulgb
That way you could serve 900 bottles. Can you serve more?

Hint: Look at the number of possible outcomes. In this case, each of the 10
mice can either live or die. That gives us 2^10 = 1024 possible outcomes. We
can only encounter 1000 possible initial configurations of bottles. Is there a
way to set it up so that each of the 1000 possible outcomes maps to an initial
configuration?

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colonhyphenp
I figured it out by thinking what would happen if you only had 1 mouse (500
bottles can make it to the party), then looking at the problem again with 2
mice (there's a way to prove that 750 bottles are poison-free using only 2
mice), etc. all the way up to 10 mice.

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gocards44
You do the mice as binary and then read them like 0's and 1's if they die or
don't die

