Returning Explorer Puzzle
Puzzle
An explorer walks:
He finds himself back where he started.
He shoots a bear.
What colour is that bear?
Variant 1
A "sportsman" who shoots things for fun decided to go out and shoot a bear.
Suddenly he saw a huge bear a hundred metres due east.
In a panic, in confusion, he ran due north for a hundred metres.
Then he caught hold of himself and stopped, and turned.
He saw the bear, which had not moved, a hundred metres due south.
Of course, he shot and killed the poor bear.
What colour is that bear?
Variant 2
An explorer walks:
He finds himself back where he started.
Where are all the places in the world where this is possible?
Solution
White.
Proof
The explorer starts from the North Pole.
Every direction from the North Pole is due south.
Walking due east keeps him the same distance (one mile) from the North Pole.
Walking due north takes him back to the North Pole again.
The bear, as a consequence, must be a polar bear.
$\blacksquare$
Sources
- 1944: Eugene P. Northrop: Riddles in Mathematics ... (previous) ... (next): Chapter Two: Paradoxes for Everyone
- 1965: Martin Gardner: Mathematical Puzzles and Diversions ... (next): Nine Problems: $1$
- 1988: Martin Gardner: Hexaflexagons and Other Mathematical Diversions ... (next): Nine Problems: $1$