Getting back to the real point of this thread, the interviewer would be making a subjective decision of which response they prefer to hear. There’s no way to know whether an interviewer wants someone who will flat-out declare the question stupid and impossible; or someone who will come up with a solution that meets 80% of the need.
Digression: this reminds me of a friend who interviewed at a big law firm, one of those cattle call sort of things. The interviewer did one of those tricks where he leads people into a series of questions that almost always end up with the same answer: pick a number from 1 to 10 and multiply it by nine, then add up the digits; etc. Who the hell knows why he was doing this.
So after the interviewer goes through the whole thing, he tells the group of applicants, “Now that you’re all thinking about the blue elephant from Denmark, we shall begin the interviews…”
My buddy stood up and said, “I have no interest in working for the Devil!” and walked out. The interviewer liked that response and called the next day to offer him a job. Goes to show that there really is no right answer to many interview questions.
The question depends on three additional implicit assumptions:
The dice must always produce a result from 2 to 12.
The range of results from 2 to 12 must include the entire set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
The dice may not be engineered to roll some sides more often than others.
If all three assumptions are in force, it is trivial to prove that the task is impossible – the dice have 36 possible rolls; the range of results has 11 members; 36 is not divisible by 11. Discarding the first assumption allows solutions such as the above described 0-0-0-6-6-6 and 1-2-3-4-5-6 dice. Discarding the second assumption allows solutions that equally distribute the results among three, six, or nine possible results. Discarding the third assumption allows for weighted dice engineered to artificially level the usual distribution.
I was going the same direction, but I assumed the dice had to be identical. (I’m not sure if having 3 1s and 3 6s on each works out, but I already have a job—which I’m supposed to be doing.)
I came in to post that I too did one of those “obstacle courses” where each stage was a sort of puzzle. For the most part, each stage was a physical variation on a sort of “Fox, Chicken & Corn” puzzle. Each stage was a little different, and finishing the course required leadership, deference and organization. At each stage, someone saw a solution and the group had to implement it.
One stage was a very physical kind of puzzle. What made it challenging was that each person had to solve it individually, and if any one person failed, everyone had to start over. It may have been a course designed for small groups; or maybe our 20 person group was just prone to emotion, but we didn’t finish the course.
I think we have to throw out # 3 totally and completely as the stipulation is:
If we are given the liberty to design both die I do not assume that means that it only means we can include pretty pictures on it.
Likewise the stipulation as stated does seem to indicate that all that is required is equal distribution for values 2-12, negating #1.
I tend to avoid pedantic arguments during job interviews, so let me just say: I admire the brevity and sagacity of your explanation, and I have always seen that as one of the strengths of this company. Do you have casual Fridays?
Fixed link
As an aside, how did you create that link? I’m not sure what would lead someone to putting in the http:// twice.
And back to the content, what axioms did he let you use? There are a wide variety of axioms which, together with Euclid’s first four, are equivalent to each other. Proving Playfair’s Axiom from Euclid’s parallel postulate is a perfectly fair question.
As a student, I occasionally ran into an impossible to answer question.
E.g., in a Calculus class, a instructor put a question on the test to integrate the elliptic function. Which is a famously impossible problem. When we asked him to solve it after the test, he hemmed, hawed, etc. Promised he’d get back to us. He didn’t last long.
Not deliberate. But on qualifying exams for a PhD one might be asked to solve an open or impossible problem. The real question was whether you would recognize it.
Back to the OP, again, I faced such a Kobayashi Maru sort of question in my upper-level undergraduate Numerical Methods class. It was either homework or a take home exam question, not sure which. I’m also unfortunately fuzzy on the details of the question, but the gist was this: Using the techniques described in class, calculate the following… and show your work.
The underlying problem had a pretty obviously correct answer. Applying the specified numerical methods to it, however, resulted in a wildly wrong answer. The point of the question was to make students aware of the weaknesses inherent in the methods being studied, but it also had a side effect of separating those who dutifully supplied the wrong answer and those who fudged things in their application of those methods to arrive at the supposedly correct result.
Those who gave the wrong answer were given credit, and those who magically gave the right answer were graded down. The whole point was to get the wrong answer, but to get it wrong correctly.
