Developer Interview Question

[Enthuse0809]

I was not able to answer this Technical Interview Logic Question
Can some one help me.

LOGIC PROBLEM -- There are three boxes. One labeled “Nickels” another “Quarters” another “Nickels and Quarters”. They are all mislabeled. How could you select ONE item from ONE box and figure out how to relabel the boxes correctly.

[laserlight]

Hint: all the boxes are mislabeled. From this, you can determine the two possibilities of what they currently contain. By picking one item from any box, you can thus rule out the other possibility for that box, which then allows you to rule out the possibilities from the other boxes.

[nuzzle]

The key to this quiz is that all boxes are mislabeled.

Say you order the three boxes according to how they're actually labeled (N=nickels, Q=quarters, N&Q=nickles and quarters) like this,

N, Q, N&Q

Now since all are mislabeled what are the alternatives to label them corrrectly? It's,

Q or N&Q, N or N&Q, N or Q

That would be 2*2*2=8 possible combinations in total but since each label can appear once only there are just two correct labelings possible,

1: Q, N&Q, N
2: N&Q, N, Q

Finally how do you decide which of these two possibilities you actually have? Well, you pick an item out of the third box labeled N&Q. If it's an N the first labeling is correct, if it's a Q it's the second.

[nuzzle]

By picking one item from any box, you can thus rule out the other possibility for that box, which then allows you to rule out the possibilities from the other boxes.

Sorry, I didn't notice you had replied while I was working out my reply.

But is your hint correct? According to my solution you must pick exactly from the box labeled N&Q to get a conclusive result. For example if you happen to pick a Q out of the N-labeled box you cannot decide which labeling is correct. Only if you get lucky and pick an N can you tell.

[laserlight]

But is your hint correct? According to my solution you must pick exactly from the box labeled N&Q to get a conclusive result. For example if you happen to pick a Q out of the N-labeled box you cannot decide which labeling is correct. Only if you get lucky and pick an N can you tell.

Ah, no, you are right to say that only picking from the box labeled N&Q are you guaranteed to be able to rule out the other possibility. (Though I could "cheat" and say that I wanted Enthuse0809 to work through a deliberately inaccurate hint instead of taking it at face value )

[Enthuse0809]

Thank you both laserlight & nuzzle. I got it now.

[MrViggy]

My favorite has always been:
You're in a room with two doors, and two other people. One door leads out, and one leads nowhere. One person in the room always tells the truth, the other person always lies. What *one* question could you ask, *one* of the other people in the room, to figure out which door leads out?



Viggy

[TheGreatCthulhu]

Could you open the exit door for me?

EDIT:
Or any door for that matter. The person doesn't have to know the right one.
But, there is a problem... A legitimate answer to that question is "No."...
D4mn...

[TheGreatCthulhu]

I know!
What would the other guy say about this door? And than pick the opposite - the one that the other guy would (supposedly) claim to "lead nowhere".

Honest  --+-----e-----L(w)-------- [exit] -------H(w)------w-----+-- Liar
           \                                                    /
            +---w-----L(e)-------- [wall] -------H(e)------e---+

[nuzzle]

It seems both quizzes have a common denominator they may share with most quizzes of this kind: There's a certain dependency between alternatives and once you "see" it the solution presents itself as obvious and trivial.

In the first quiz, given that all boxes are mislabeled, by drawing an item from the N&Q box there's just one labeling possible.

In the second quiz, given that both other persons know whether the other is a liar or not and they're asked to ask each other, whoever you ask the reply will be a lie.

The big quiz here I'd say is whether quizzes like these have a place in an interview for programmer? I don't think so because they're based on a moment of laid-back enlightment. If you're familiar with the quiz you'll look like a genius but if not even an Einstein may run into trouble in a stressful interview situation.

[laserlight]

The big quiz I'd say here is whether quizzes like these have a place in an interview for programmer? I don't think so because they're based on a moment of laid-back enlightment. If you're familiar with the quiz you'll look like a genius but if not even an Einstein will get into trouble in a stressful interview situation.

Yeah, on one hand, there's the element of constraint programming, and if the candidate were to think out loud, the interviewer can get an idea of the candidate's logical thinking skills even if he/she gets stuck or comes up with a wrong answer; on the other hand, it can be considered one of those trick puzzles where you're either very lucky to see the solution, or you know the solution beforehand, neither of which tells the interviewer anything about the candidate's logical thinking skills.

[TheGreatCthulhu]

Which means that in such cases it all boils down to whether the person conducting the interview qualifies for his own job of an interviewer, and indeed what are the intentions behind the question.
If the purpose behind it is to make a preliminary assessment of candidate's logical thinking skills, possibly important for the job - then it's not a big deal. EDIT: Actually, a fair thing to do would be to inform the candidate that it is not necessary to produce the solution to the next question, and that the purpose is to perform a little exercise logical reasoning.
If it's a can-you-meet-my-out-of-nowhere-criteria test, where the criteria are based on personal unfounded assumptions, or some supposedly generic quick-and-easy candidate litmus test - then there's a problem, and no place for the question in the interview.

Which makes me wonder: Enthuse0809, were you practicing for a future interview, or did this happen on an actual interview? If the latter, how did the interviewer react?