There is a game played between the easter bunny VERSUS a team of 4 kids. I will fully explain the rules of the game below. However, I'd like to start with the preface.
I found this problem as a king of the hill puzzle in codegolf.se. King of the hill here means that, as a programmer, your answers are programs that compete with each other. In this case, if you make an easter bunny algorithm, it will compete with all other kids' algorithms, and vice-versa. Now the interesting thing is that this specific topic got very few answers, which is unusual. That drives me to think that there was a "kind of trivial" solution, and that's why I'm posting it here.
For the rules that follow, is there any algorithm for either the bunny or the kids, that defeats its opponent no matter the opponent's algorithm? If so, please present it; if not, please prove it.
Rules of the game (copy/paste from OP)
The garden is a 2-dimensional grid with 49 rows and 49 columns.
The Easter Bunny™️ is in the center of the garden, minding his own business, holding on to 100 Easter eggs.
Unfortunately, there's a team of 4 children who aren't content to collect chocolate eggs, they want to capture the Easter Bunny™.
The game starts with 4 kids, one in each corner of the garden.
The kids can take 1 step each turn, in one of the 4 cardinal directions (North, South, East or West). When they've each taken a step (or decided not to), the bunny will take a move.
The kids can only see the Easter Bunny or it's eggs when they are 5 steps away or nearer.
Kids visibility (yellow) and movement options (green):
The bunny can hop up to 2 spaces away on both axes (describing a 5 x 5 square he can hop to). Each time the bunny hops, it leaves behind an Easter egg.
The Easter Bunny™ can only see the kids when they are 5 steps away or nearer.
Bunny's visibility (yellow) and movement options (green)
Neither kids nor the Easter Bunny™ can leave the garden.
The game ends when:
- The Easter Bunny™️ drops his last egg.
- The kids catch the bunny.
- The game reaches turn 1000.
- The Easter Bunny™ wants to give the children as many Easter Eggs as possible while evading capture.
- The kids want to collect as many eggs as possible, AND catch the Easter Bunny™.
This means that:
- The Easter Bunny™ will ONLY score points if it evades capture by dropping it's last egg, or by finishing the time limit.
- The team of kids will ONLY score points if they capture the Easter Bunny™.
- In either case the points scored is the number of eggs the kids have picked up.
- The bunny may chose not to move (Deduction source: green central tile on bunny's move map)
- If it chooses to move, it must drop an egg on its departure tile, which may already contain any number of eggs. The bunny may chose to move into a tile which already has eggs on it. (Deduction source: found nothing to the contrary)
- The kids have instant telepathy unlimited by range (Deduction source: the kids' API is one, not four, so the programmer can use any data from other kids to move one)