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MisterEman22
MisterEman22
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EDIT:

I guess a better way to word this would be that the single lion goes toward the center zebra of 3 that are closest together, angle-wise. No matter how the zebras are set up, at least 3 zebras must be adjacent and separated by angles of 3.6 degrees or less. One zebra could be on the opposite side of the lions from the other zebras, in which case the lion would go for a zebra that has the least sum of angles between itself and the two adjacent zebras. If the zebras were separated by 3.6 degrees each, then this would be the optimal strategy for them, however they would still lose. They wouldn't lose if this angle is greater than or equal to 90 degrees, because no matter how far out the lion goes, it's distance to cut off any zebra will always be longer than the distance the zebra must go to get to that same point, so it will never catch any of the zebras. For any angle less than 90 degrees between each zebra, the lion can get to a point far enough away from the circle that it will be able to "cut off" one of the adjacent zebras to the one it was following. If the adjacent zebra that the lion targets decides to cut over, it will be cutting into the path of another one of the zebras, and if two of these zebras are in the same path, then it will be simple for a lion to get one of them because the lion can move 200m for each 100m moved by each zebra.

EDIT:

I guess a better way to word this would be that the single lion goes toward the center zebra of 3 that are closest together, angle-wise. No matter how the zebras are set up, at least 3 zebras must be adjacent and separated by angles of 3.6 degrees or less. One zebra could be on the opposite side of the lions from the other zebras, in which case the lion would go for a zebra that has the least sum of angles between itself and the two adjacent zebras. If the zebras were separated by 3.6 degrees each, then this would be the optimal strategy for them, however they would still lose. They wouldn't lose if this angle is greater than or equal to 90 degrees, because no matter how far out the lion goes, it's distance to cut off any zebra will always be longer than the distance the zebra must go to get to that same point, so it will never catch any of the zebras. For any angle less than 90 degrees between each zebra, the lion can get to a point far enough away from the circle that it will be able to "cut off" one of the adjacent zebras to the one it was following. If the adjacent zebra that the lion targets decides to cut over, it will be cutting into the path of another one of the zebras, and if two of these zebras are in the same path, then it will be simple for a lion to get one of them because the lion can move 200m for each 100m moved by each zebra.

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MisterEman22
MisterEman22
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The lions will win.

Because:

Assuming the zebras take their optimal strategy, which would be to create a circle an arbitrary distance out from the center of the lions. Let's say that the zebras make such a large circle that any distance a lion is from the center is negligible, so we can say they are all at the direct center of the circle. This will look like this:enter image description here
with the lions at the red dot in the center (assume its a point, as explained above) and the zebras around the circle.

When they move:

A single lion moves directly north, going for the zebra at that spot on the circle (let's call it zebra A). That zebra would in turn move away, and the lion would keep moving in that direction. At some point, the lion would be closer to one of the adjacent zebras to the one it is following (let's call them B and C), however it would keep moving in a straight line toward the original zebra. To keep safe, all three of those zebras would have to move out in their respective path. For this lion strategy, the lion would keep moving in the straight line following zebra A, so B and C could stay in the same spot, but that doesn't matter. Either way, the lion would get far enough outside the original circle (if B and C don't move) or the arc that B and C make (if they move in their respective paths) that it would either catch up to A or get to a point where it can get to a point that is in between B/C and the center of the circle. If it catches up to A then the lions would obviously win. If it gets to a point that is on the opposite side of B/C and the center of the circle (all the other lions), then it would have that zebra trapped. So the lions win. Here are a couple pictures to explain:enter image description hereenter image description here
The only other thing that the zebras could do is have B and C each move out of their path (the straight path from the center of the circle). If this were to happen, they would eventually get in the way of the zebra that is on that side of them. In this case the lion could just go straight toward those zebras, and having both zebras in a (relatively) close location, they would be trapped because the lion could move faster (only one lion and two zebras escaping, so lion moves 100m and then each zebra must move 100, so lion moves 200 for each 100 per zebra).