Polar Bear Puzzle

By Susam Pal on 09 Mar 2011

Alice asked Bob, "A bear walked 1 km south, then 1 km west, then 1 km north, and it was back at the point from where it started. What colour was the bear most likely to be?"

Bob thought for a while, could not arrive at an answer, and gave up. Alice explained, "Well, the answer is white. It is a polar bear. It is only when you start from the North Pole that after travelling 1 km south, 1 km west, and 1 km north you would end up at the point where you started."

Bob replied, "That is an interesting solution. Now that I understand your solution, I realize that there are other starting points apart from the North Pole where one could walk 1 km south, then 1 km west, and then 1 km north to return to the starting point."

Can you find all the other such starting points that Bob is talking about?

See the comments page for the solution.