This a variation of [this question][1] by @Gamow

Suppose there are $100$ lions and $100$ zebras. The lions place themselves first on an infinite plane, and the zebras place themselves next. Game proceeds turn-wise. On each turn, a single zebra or lion moves by upto $100$ metres. Lions win if a single zebra is eaten.

Zebras will try to ensure this doesn't happen. Do the lions' have a strategy that works irrespective of the zebras' one?

P.S. @Veedrac's result is definitely helpful (whether or not you understand the math) if you are attempting to solve this.


  [1]: http://puzzling.stackexchange.com/questions/9036/the-lion-and-the-zebras