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(This is the continuation of an article about the use and abuse of brainteasers in job interviews. This page contains the first of three examples drawn from actual interviews.)
The problem, as posed, reiterated:
"A man is out hunting. He walks one mile south. He makes a
degree turn to his left. He walks another mile. He makes another ninety
degree turn to his left and walks another mile. He is now back where he first started. He shoots a bear. What color is the bear?"
Let me start by saying, glibly, that if one assumes there is a correct
solution to this problem, then there is only one possible answer:
"white". The only place on earth where the directions you
would be a
clue about the color of a bear would be if they mean you are near the pole, so it must a polar bear.
Duly clever, but, as the problem is stated, simply wrong. There is no
way to know whether this problem was deliberately mis-stated, but presumably the correctly phrased brainteaser is:
"A man is out hunting. He walks one mile south. He turns and walks one mile east. He turns again and walks one mile north. He is now back where he first started. He shoots a bear. What color is the bear?"
Why is the original problem misstated? Because, as any surveyor can
tell you, near the pole, a turn from facing south to facing east is not even close to ninety degrees. Only at the equator is it exactly ninety degrees. Here in the latitudes where most of us live, ninety degrees is a
"close enough" approximation, but this is why a Mercator projection gets so stretched in the polar regions.
If you think about it carefully, the curvature of the earth is almost perfectly uniform (marred more by mountain ranges than by anything that is relevant to this problem). Regardless of where you start, if you actually walk one mile south, make a ninety degree turn to your left, walk another mile, make another ninety degree turn to your left and walk another mile, you are not back where he first started. You are almost exactly a mile from where you started (the curvature of the earth means you are the tiniest bit off of a mile). The only difference about starting from the north pole is that any direction you first walk qualifies as south.
As is happens, the candidate was familiar with the correctly stated
problem, and immediately smelled something wrong about how it was stated
"ninety degrees", etc.). He said,
"Well, I think
your problem is wrong." The interviewer insisted his problem was
"And this is a real mile, on the real Earth?"
The interviewer assured him it was.
"I can make this work on a tiny globe where it's only one mile from the Pole to the Equator." No, the interviewer assured him, it's on the real Earth.
"I know a problem a lot like that which is going to mean you have to be at the North Pole, so it has to be a polar bear, but I don't think it works the way you've stated it."
The interviewer insisted his problem was correctly framed. The candidate, who was of course still thinking this all through, tried to explain it in an (inevitably) muddled way, the interviewer didn't give him enough time to explain, and they probably each went away thinking the other was a fool.
My guess is that most of you reading this have at least a certain affection for brainteasers, even if not in job interviews, so I'm going to go back to the correctly stated problem, get rid of the bear, and ask a slightly different, and I think somewhat interesting brainteaser:
A man is out hunting. He walks one mile south. He turns and walks one mile east. He turns again and walks one mile north. He is now back where he first started. This is all on planet Earth, but it's nowhere near the North Pole. Where could it be?Solution >>>
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