I don't really like that because it's obviously a troll question. Its wording and a large number of significant digits clearly demands the acceleration of gravity to be reverse-engineered, so it can't be a real question even by a chance. One thing to consider if it's indeed real: how much water is in that well?
Given the viscosity of air vs. water, one might assume there's no water in the well. Also, given some surface area of a bear, and air pressure from a cushion of air formed under the falling bear, the fall speed does seem a little high, at least for a calculation with that number of decimal places, but perhaps the well was located in the crust of the earth where gravity's a tad higher.
Living bears are also buoyant, and will be slowed down considerably on meeting the water, so the bear is unlikely to have reached the bottom of a water-filled well for a long period, if at all.
To answer OP, I'd say the bear is brown, because of the mud from the base of the (somewhat empty) well. However to an outside observer, given the lack of light in the well the shade of brown might not be discernable. A human in the well with the bear will see the colour of the bear as a low relative concern compared to A) being in a well and B) being in a well with a bear.
One variant of this question was designed to test the theory that students try to fit the inputs to an answer regardless of whether the answer has anything to do with the question.
People see this as some sort of failing of students but I think it says more about the teachers. You’ve overtrained students on problems that mean nothing to them, then you throw another nothing problem at them that’s simply three times as much nothing as the usual level of irrelevance.
Randall Monroe said it best: we should be teaching high school students how to split the bill for a birthday dinner. That’s more complicated math than most 20 year olds can correctly manage. It’s also what they’re going to do with math about 75% of the time.
Fur is probably pretty low-friction to begin with. Also, bears presumably have wax glands in their skin like other mammals, so if the bear hasn't showered very recently that would lessen the friction even more.
