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.