Some nice responses to my questions, well done! To clarify a few matters:
There are a few assumptions for this problem:
1. The Earth can be assumed to be a perfect sphere of radius ≈6400km (the exact value is not important).
2. West/East are along the lines of latitude.
3. North/South are along the lines of longitude.
4. The Arctic Circle is defined to be the area of the Earth more than 66°33’ North.
Because of this, there probably exist solutions where the starting point is within 1km of the North Pole, but the ideal solution(s) exist where the bear starts more than 1km from the North Pole (so it never crosses the pole). Have fun!
You must consume exactly one red pill and exactly one blue pill (to within about a quarter of a pill each). Taking more pills than this is an overdose and will kill you…