A site for technical interview questions, brain teasers, puzzles, quizzles (whatever the heck those are) and other things that make you think!
Two MIT math grads bump into each other at Fairway on the upper west side. They haven’t seen each other in over 20 years.
the first grad says to the second: “how have you been?”
second: “great! i got married and i have three daughters now”
first: “really? how old are they?”
second: “well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”
first: “right, ok.. oh wait.. hmm, i still don’t know”
second: “oh sorry, the oldest one just started to play the piano”
first: “wonderful! my oldest is the same age!”
Problem: this year on October 2, 2001, the date in MMDDYYYY format will be a palindrome (same forwards as backwards).
10/02/2001
when was the last date that this occurred on? (see if you can do it in your head!)
olution: we know the year has to be less than 2001 since we already have the palindrome for 10/02. it can’t be any year in 1900 because that would result in a day of 91. same for 1800 down to 1400. it could be a year in 1300 because that would be the 31st day. so whats the latest year in 1300 that would make a month? at first i thought it would be 1321, since that would give us the 12th month, but we have to remember that we want the maximum year in the 1300 century with a valid month, which would actually be 1390, since 09/31 is a valid date.
Problem: you are given a sequence of numbers from 1 to n-1 with one of the numbers repeating only once. (example: 1 2 3 3 4 5). how can you find the repeating number? what if i give you the constraint that you can’t use a dynamic amount of memory (i.e. the amount of memory you use can’t be related to n)?
what if there are two repeating numbers (and the same memory constraint?)
Five pirates have 100 gold coins. they have to divide up the loot. in order of seniority (suppose pirate 5 is most senior, pirate 1 is least senior), the most senior pirate proposes a distribution of the loot. they vote and if at least 50% accept the proposal, the loot is divided as proposed. otherwise the most senior pirate is executed, and they start over again with the next senior pirate. what solution does the most senior pirate propose? assume they are very intelligent and extremely greedy (and that they would prefer not to die).
100 fogcreek programmers are lined up in a row by an assassin. the assassin puts red and blue hats on them. they can’t see their own hats, but they can see the hats of the people in front of them. the assassin starts in the back and says “what color is your hat?” the fogcreek programmer can only answer “red” or “blue.” the programmer is killed if he gives the wrong answer; then the assassin moves on to the next programmer. the programmers in front get to hear the answers of the programmers behind them, but not whether they live or die. they can consult and agree on a strategy before being lined up, but after being lined up and having the hats put on, they can’t communicate in any way other than those already specified. what strategy should they choose to maximize the number of programmers who are guaranteed to be saved?
A bad king has a cellar of 1000 bottles of delightful and very expensive wine. A neighbouring queen plots to kill the bad king and sends a servant to poison the wine. (un)fortunately the bad king’s guards catch the servant after he has only poisoned one bottle. Alas, the guards don’t know which bottle but know that the poison is so strong that even if diluted 1,000,000 times it would still kill the king. furthermore, it takes one month to have an effect. The bad king decides he will get some of the prisoners in his vast dungeons to drink the wine. Being a clever bad king he knows he needs to murder no more than 10 prisoners – believing he can fob off such a low death rate – and will still be able to drink the rest of the wine at his anniversary party in 5 weeks time.
You have three jars that are all mislabeled. one contains peanut butter jelly beans, another grape jelly jelly beans, and the third has a mix of both (not necessarily a 50/50 mix, could be a 1/99 mix or a 399/22 mix). how many jelly beans would you have to pull out, and out of which jars, to find out how to fix the labels on the jars?
Problem: this one is a classic that many of you have probably already heard, but all the more reason why it should definitely be included here. four people are on this side of the bridge. the bridge will be destroyed by a bomb in 17 minutes. everyone has to get across before that. problem is that it’s dark and so you can’t cross the bridge without a flashlight, and they only have one flashlight. plus the bridge is only big enough for two people to cross at once. the four people walk at different speeds: one fella is so fast it only takes him 1 minute to cross the bridge, another 2 minutes, a third 5 minutes, the last it takes 10 minutes to cross the bridge. when two people cross the bridge together (sharing the flashlight), they both walk at the slower person’s pace. can they all get across before the bridge blows up?
A slightly different version of the original pirates problem (read that one first to get all the rules). 6 pirates, only one gold coin. as before, the pirates are super-smart, and they value, in this order: (i) their lives, (ii) getting money, (iii) seeing other pirates die. so if given the choice between two outcomes, in which they get the same amount of money, they’d choose the outcome where they get to see more of the other pirates die. how can pirate 6 save his skin?