Here are the extra answers to The Bear Hunter Puzzle.

He walks a mile south, and at that point he is 0.159 miles from the south pole. This just happens to be the radius of a circle with a circumference of one mile, so when he walks a mile east, he walks round in a complete circle and gets back to the same spot. He then walks a mile north and gets back again!
The hunter starts 1.159 miles from the SOUTH POLE!

Now we did promise you an INFINITE number of places he could start from, and of course he could start anywhere on the circle with a radius of 1.159 miles from the south pole. That gives you an infinity of starting places, but we can do better than that!

Suppose he starts 1.07958 miles from the south pole. First he walks a mile south and he's 0.079577 miles from the south pole. This is the radius of a circle with a circumference of *half* a mile, so when he walks one mile east, he goes round the same circle twice! He then heads north again.

And if he started 1.05305 miles from the south pole he'd go round in a circle *three* times... and so on!

In fact if he started exactly one mile from the south pole, he'd walk south, spin round an infinite number of times on the spot and then get back... if he wasn't too dizzy to know which way to go!