techinterview

At 6 a.m. a man starts hiking a path up a mountain. he walks at a variable pace, resting occasionally, but never actually reversing his direction. at 6 p.m. he reaches the top. he camps out overnight. the next morning he wakes up at 6 a.m. and starts his descent down the mountain. again he walks down the path at a variable pace, resting occassionally, but always going downhill. at 6 p.m. he reaches the bottom. what is the probability that at some time during the second day, he is in the exact same spot he was in on the first day?

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You find an old treasure map in your grandma’s attic. the map shows a cannon, a coconut tree, and a palm tree. the map states that to find the treasure you must:

a. start at the cannon, walk toward the palm tree while counting your paces. when you reach the palm tree, turn 90 degrees to your left and walk the same number of paces. mark that spot on the ground with a stake.

b. start at the cannon again, walk toward the coconut tree while counting your steps. when you reach the coconut tree, turn 90 degrees to your right and walk the same number of paces. mark that spot on the ground with a stake.

c. find the midpoint between the two stakes and dig for the treasure.

you set off in secrecy to the deserted island. upon reaching the shore you site the coconut tree and the palm tree, but someone has removed the cannon. without digging randomly all over the island, is it still possible to find the treasure?

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A. first i would just like to say i am so glad jenna got voted off survivor. yuck, i couldn’t stand her ever since she accused that guy of eating beef jerky when he was chewing on grass.

B. recruit meyer on boot camp rocks. did you see how he made himself cry to get sympathy? and it worked! he is the funniest part of the show. i hope he wins.

C. i apologize for this site being soooooo slow. but that’s why you get what you pay for. (i didn’t pay anything so i shouldn’t really expect anything in return.)

D. those screwy pirates are at it again. this time there are 13 pirates and they need to protect their treasure chest. they decide that they should only be able to open the chest if the majority (at least 7) agree that it should be opened. they ask a locksmith to come and put a specific number of locks on the safe. every lock must be opened to open the chest. there can be multiple keys for each lock, but each key only opens one lock (i.e. no skeleton keys). the locksmith can give more than one key to each pirate. how many locks should the locksmith use and what strategy should he use to distribute the keys, such that only when a majority of the pirates agree can the chest be opened?

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There are three ants on a triangle, one at each corner. at a given moment in time, they all set off for a different corner at random. what is the probability that they don’t collide?

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How many places are there on the earth that one could walk one mile south, then one mile east, then one mile north and end up in the same spot? to be precise, let’s assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere and walk in any direction you like.

think you’ve figured it out? i’ll tell you now, there is more than one. in fact, there are more than two. also be advised that walking north from the north pole (or south from the south pole) is illogical and therefore does not enter into the problem. all normal assumptions about directions will be used.

there are no tricks involved with this question. it just forces you to really think about the problem to come up with all the solutions.

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This is difficult to describe in words, so read this carefully, lest there be any confusion. You have a normal six sided cube. i give you six different colors that you can paint each side of the cube with (one color to each side). How many different cubes can you make?

Different means that the cubes can not be rotated so that they look the same. This is important! If you give me two cubes and I can rotate them so that they appear identical in color, they are the same cube.

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I buried four fishermen up to their necks in the sand on the beach at low tide for keeping their fishing spot a secret from me. I put a hat on each of their heads and told them that one of them must shout out the correct color of their own hat or they will all be drowned by the incoming tide. I give them 10 minutes to do this. Fisherman A and B can only see the sand dune I erected. Fisherman C can see that fisherman B has a white hat on. Fisherman D can see that C has a black hat, and B has a white hat. The fisherman have been told that there are four hats, two white and two black, so they know that they must have either a white or a black hat on. who shouts out the color of their hat and how do they know?

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You die and the devil says he’ll let you go to heaven if you beat him in a game. the devil sits you down at a round table. he gives himself and you a huge pile of quarters. He says “ok, we’ll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. The first guy who can’t put a quarter down loses.” the devil says he wants to go first.

Being the smart programmer you are, you realize that if the devil goes first, he may automatically win. so you convince him to let you go first, which makes your day because you know you can’t lose. what is your winning strategy?

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There is a pot of N noodles. (so there are 2N ends). A person randomly grabs two ends and merges them. The person keeps doing it, until there are no more noodles, (and only loops), left in the pot. what’s the average number of loops in the pot?

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A person dies, and arrives at the gate to heaven. there are three doors. one of them leads to heaven. another one leads to a 1-day stay at hell, and then back to the gate, and the other leads to a 2-day stay at hell, and then back to the gate. every time the person is back at the gate, the three doors are reshuffled. How long will it take the person to reach heaven?

this is a probability question - i.e. it is solvable and has nothing to do with religion, being sneaky, or how au dente the pasta might be ;-)

Solution

1/3 of the time, the door to heaven will be chosen, so 1/3 of the time it will take zero days. 1/3 of the time, the 1-day door is chosen; of those, the right door will be chosen the next day, so 1/9 trips take 1 day. Similarly, 1/9 will take two days (choosing the 2-day door, then the right door).

After that, the cases split again, and again, and again. I can’t seem to make a nice infinite sum this way, so let’s try again.

Suppose the average days spent is X. 1/3 of the cases are done in zero days as before. 1/3 of the cases are 1 day plus X. 1/3 are 2 + X. So:

X = 1/3 * 0 + 1/3 * (1 + X) + 1/3 * (2 + X)
  = 0 + 1/3 + X/3 + 2/3 + X/3
  = 1 + 2X/3

Therefore,

  X/3 = 1
    X = 3

On average, it takes three days to get to heaven. Two if the noodles are limp.

Took me one blind alley, and about five minutes. (heh heh)