alt Hacker NewsI did see a game recently which did that (you place a tile, the animal moves a tile, etc.) - possibly on itch.io. I'll see if I can dig it out.
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I remember a game I played on my phone ~15 years ago called "Greedy Spiders". The spiders would move greedily towards something every move, but you could cut strings in their web so they would have to start a new route. So you would kinda have to lure them into going one direction while slowly chipping away at the web, until you could completely cut them off or force them to have to take a longer detour giving you more time to cut more of the web. Quite challenging after a while.
A Windows 3.1 game called Rodent's Revenge: https://classicreload.com/win3x-rodents-revenge.html
Video: https://www.youtube.com/watch?v=-r6CnPzTXKE
Damn, the good old days when games didn't have loot boxes, ads, etc...
There's an old Flash game called 'Chat Noir' where you have to trap a cat on a hexagonal grid. Here's a copy of it: https://www.hoodamath.com/games/chatnoir.html