The lion plays a deadly game against a group of 100 zebras that takes place in the steppe (an infinite plane). The lion starts in the origin with coordinates (0,0), while the 100 zebras may arbitrarily pick their 100 starting positions. The the lion and the group of zebras move alternately:
- In a lion move, the lion moves from its current position to a position at most 100 meters away.
- In a zebra move, one of the 100 zebras moves from its current position to a position at most 100 meters away.
- The lion wins the game as soon as he manages to catch one of the zebras.
Will the lion always win the game after a finite number of moves? Or is there a strategy for the zebras that helps them to survive forever?
The zebras can survive forever. They choose 100 parallel strips with width 300m each, then start on points on their mid-lines. If the lion lands on some zebra's strip, the zebra simply jumps 100m away from the lion, along its mid-line.