Top Companies Interview Problems/ Puzzles

silverblue · #41 01-01-2004

This is a smart question! I am not sure but lemme try...

I guess bcos the contaminated pill weighs 9 grams, we can find the answer by looking at the multiples of 9 as the total weight of the scale. But we have to take 1 pill from the first jar, 2 from the 2nd, 3 from the 3rd, 4 from the 4th and 5 from the 5th.... so that we know that the last digit of the total weight of these pills gives away which jar is contaminated. Example, if the last digit is 9, u know it's from jar 1. If the last digit is 8, it is jar 2. If the last digit is 7, it is jar 3. If the last digit is 6, it is jar 4 and if the last digit is 5, it is the last jar...

just trying..

silverblue · #42 01-01-2004

Opps, I think Luke got to it a few mins faster than I did... but I'm glad we got the same concept!

**luke** · #43 01-01-2004

I'd like to modify Question 5 and propose this question:

There are 5 jars of pills. All the pills in two of the jars are contaminated. The only way to tell which pills are contaminated is by weight. A good pill weighs 10 grams while a contaminated pill in one jar weighs 9 grams while a contaminated pill in the other jar weighs 8 grams.
You are given a scale and allowed to make only one measurement with it. How do you tell which jars are contaminated? If possible point out which one is 8 grams and which one is 9 grams.

There.

Hint: The solution is similar to the answer of the original question where you take a certain number of pills from each jar and weigh them. However, in this question the number of pills from each jar is not 1,2,3,4 and 5 but more discrete. You have to figure that out. To make life easier, you can use this javascript I created to test your answer : http://anatilmizun.homeip.net/pills.php

littlebigone · #44 01-01-2004

Quote:

Originally Posted by luke

Quote:

Originally Posted by littlebigone

Then if say we break on floor 20, we will need to take the unbroken ball and test on floor 21, 22, 23, and 24. Obviously we would stop as soon as that ball breaks and that would be the floor.

and obviously if the ball breaks on floor 20, it will break if dropped from level 21,22,23 or 24

... the higher, the harder it will hit ..

you should choose floor 19, 18, 17 and so on for the 2nd ball .. but what if the 2nd ball breaks on floor 19? can we conclude that k=19? No! We know the ball doesn't break on floor 15 but what about floor 16, 17 and 18? We don't know if the ball also breaks if dropped from those floors but unfortunately we only have 2 balls (yes some of us do

) and both of them are gone (oh no!) .. so how?

oops....meant to say 16, 17, 18, 19...hehehe...which now means that the max tests should be 14

mpalanieppan · #45 02-01-2004

for luke's question i think instead of 1,2,3,4,5 subs with 2,3,5,11,29. This sequence has the property that the answers produced by 2a+b, a+2b for any a and b from those 5 numbers have distinct answers for all a's and b's and thus eliminate ambiguity

Btw, usually how much time would be given to answer these questions during interview?

huilinchin · #46 03-01-2004

Sorry for the long absense. I have been busy at home and will be flying back to the US in less than a week.

I think not more one minute will be given to answer most of the questions. However, we do not need to answer the questions at once, but do it step by step by reasoning. Explanation and reasoning are more important although a correct final answer will be impressive.

Bear in mind that this is only one small session of the interviews. I am very glad that there are many ReCom members here who can answer the puzzles here accurately and are potential employees of top companies.

Actually, my main reason for creating this thread is not only to create awareness of such a test in job interviews, but also to encourage and cultivate logic and creative thinking in everyone. I feel fortunate to be given the chance to learn these puzzles and hope that others who have been reading this thread will contribute by sharing interview questions/ puzzles that they have encountered in interviews.

Thanks, luke for modifying the question, making it more challenging. I hope others can do the same by posting edited questions that have been asked.

Please feel free to email new questions to [email address]

so that we can organize this forum thread better.

Big applause again to luke and silverblue for correctly answering the Question 5.

Answer for Question 5 quoted from luke:
just get one pill from jar 1, 2 pills from jar 2, 3 pills from jar 3 .. continue for jar 4 and jar 5 .. then put all those pills on the scale and get the reading .. the jar with contaminated pill is (150-reading) .. so if the reading is 148 then the contaminated jar is jar 2 ... if it's 149 then it's jar 1 ... if it's 150 then the scale is broken and should be replaced, or all the pills are safe and you are overcautious

Thanks for trying!

-Hui Lin ^_^

huilinchin · #47 03-01-2004

I come across a book called "How would you move Mount Fuji" recently by William Poundstone and find it pretty interesting.
I am going to share a couple of questions from the book.

Question 6:
Source: One of the assignment problems given by Steven Rudich in CMU.
Also appeared in the book quoted above.

5 pirates on an island have one hundred gold coins to split among themselves. They divide the loot as follows:
The senior pirate proposes a division, and everyone votes on it. Provided at least half the pirates vote for the proposal, they split the coins that way. If not, they kill the senior pirate and start over. The most senior (surviving) pirate proposes his own division plan and they vote by the same rules and either divide the loot or kill the senior pirate, as the case may be. The process continues until one plan is accepted. Suppose you are the senior pirate. What division do you propose? (The pirates are all extremely logical and greedy and all want to live)

Happy trying!

-Hui Lin ^_^

jiinjoo · #48 03-01-2004

I thought the question used to say that the pirates were splitting gold bars instead of coins and they all have a computer science degrees from CMU?

Not fair for me to solve this - just thought it was one of those questions that kept me awake at night to work on it without avail, but after good long sleep, I'll wake up and say to the world "Ahah!!" and suddenly my world has changed. This is really a classic mind teaser.

**chenchow** · #49 03-01-2004

Personally I would think that we need to get the votes from at least 2 of the pirates, since if I am the senior, I will vote for it, and that would give the majority of vote.

So, I think a division of 33 each for 3 of the pirates, including ownself will be sufficient. Since, these 3 votes will be sufficient right? but it may be a little bit too cruel...

Thanks a lot, Hui Lin for sharing all these questions!

**luke** · #50 04-01-2004

chenchow is being greedy ... he even takes the remaining 1 percent

silverblue Member Join Date: Jun 2003 Posts: 260	#42 01-01-2004 Opps, I think Luke got to it a few mins faster than I did... but I'm glad we got the same concept!

mpalanieppan Super Junior Member Join Date: Apr 2003 Posts: 35	#45 02-01-2004 for luke's question i think instead of 1,2,3,4,5 subs with 2,3,5,11,29. This sequence has the property that the answers produced by 2a+b, a+2b for any a and b from those 5 numbers have distinct answers for all a's and b's and thus eliminate ambiguity Btw, usually how much time would be given to answer these questions during interview?

luke KittyLover Administrator Join Date: Nov 2003 Posts: 1,878	#50 04-01-2004 chenchow is being greedy ... he even takes the remaining 1 percent __________________