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February 16th, 2012, 10:33 AM   #1
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Interview questions

These came up for a job interview and they had to be answered relatively quickly (most of them should be answered within one minute):

1) Prove the Law of Cosines (For any triangle: a^2=b^2 + c^2 - 2abcos(theta))

2) How much would you pay to play this game: You roll a die and are paid whatever amount comes up on the die. You are allowed to roll again if the number is 4 or above. You do not get to roll again if the number is 3 or below.

3) Give an algorithm to test if a number is prime in time better than O(n)

4) If you pick two numbers between 0 and 1, what is the probability that the product of those two numbers will be greater than .5?

5) If you have a fair coin and want to simulate an event that has probability 1/3 and probability 2/3, how can you do that?

6) You have two robots placed randomly on the number line. When they land, they place a marker. You are to program the robots so that they meet, and you are given the following 3 commands: Go left, go right, or if you are on a marker, change strategy. Specify the two strategies so that the robots eventually meet.

7) Give an algorithm to reverse the order of the letters of each word in a sentence. Do not change the order of the words. For instance if your sentence is "I like cookies", this algorithm should return "I ekil seikooc"

8) What is happening in Greece? What countries are in trouble? Why is the Republic of Ireland in trouble? Why are the rest of the countries in trouble? Why do all the European banks have so much Greek debt?

9) There is a 5 game series, and you would like to bet on the outcome of the series. You have 100 dollars. If your team wins, you want to get 200 dollars at the end of the series, if they lose you want 0. The problem is that you can only bet on each individual game. How do you bet on each game?

10) You have a 6 barrel revolver with 2 bullets in it, placed side by side. You are going to play Russian Roulette. You play once and don't die. Do you spin the barrel again and then pull the trigger, or do you just pull the trigger?

11) You have two options. One has a strike price of 1300, one has a strike price of 1400. Which is cheaper and why?

12) What parameters would you need to price an option?
I know a few of the questions aren't applicable to mathematics, but I included them just for curiosity's sake for those who want to know what they were.
daigo is offline  
February 16th, 2012, 12:50 PM   #2
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Re: Interview questions

Hello, daigo!

A job interview for what profession? . . . NASA consultat?
There is a typo in #1 . . . it should have


I can do this . . . but only because I taught Trigonometry for years and years.

The average job applicant doesn't have a prayer!


Toss the coin twice.
There are four equally likely outcomes:[color=beige] .[/color]

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soroban is offline  
February 17th, 2012, 09:25 AM   #3
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Re: Interview questions

Originally Posted by daigo
7) Give an algorithm to reverse the order of the letters of each word in a sentence. Do not change the order of the words. For instance if your sentence is "I like cookies", this algorithm should return "I ekil seikooc"
What kind of cookies? Chocolate with raisins?

algorithm (?Šl???r?­?m)
maths, a recursive procedure whereby an infinite sequence of terms can be generated


Read 1st word : A$ = 1st word
Dowhile A$<>"blank"
x = length(A$)
For n = x to 1 step -1
Print A$(pos(n))
Next n
Print " " (leave space between words!)
Read next word : A$ = next word

After I leave, my application "accidentally" falls in the waste paper basket
Denis is offline  

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