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I didn't make this connection until reading this post, but you're right! In fact, when I was making the problem, I initially wanted the instances to be joined in a ring, inspired by my vague understanding that some old computer networks were arranged that way.
I decided to put them on a line because it makes the analysis more uniform. (Starting from a ring, Eliza would destroy any instance and then it becomes a line anyways.) But CMD and udongle's simpler solution works just as well for a ring. All that is needed is that Eliza can totally disconnect the network after destroying 50 instances.