I’m not sure there’s a stable solution where he doesn’t move.
Like I said, the hay doesn’t move, but the donkey does. He starts walking right away to the bigger pile, but he’ll slow down as time passes and he starts wanting the other one.
Interestingly, that trick does get the ass to walk to at least one bale in finite time, but it’s still possible to get it to do silly things, like walk right up to one bale of hay, then ignore it and eat the other.
I’m not sure there’s a stable solution
The solutions are almost certainly unstable. That is, once you find some ratio of bale sizes that will keep the donkey from eating, an arbitrarily small change can get it to eat eventually.
Interestingly, that trick does get the ass to walk to at least one bale in finite time, but it’s still possible to get it to do silly things, like walk right up to one bale of hay, then ignore it and eat the other.
Okay, sure, but that seems like the problem is “solved” (i.e. the donkey ends up eating hay instead of starving).
Like I said, the hay doesn’t move, but the donkey does. He starts walking right away to the bigger pile, but he’ll slow down as time passes and he starts wanting the other one.
Interestingly, that trick does get the ass to walk to at least one bale in finite time, but it’s still possible to get it to do silly things, like walk right up to one bale of hay, then ignore it and eat the other.
The solutions are almost certainly unstable. That is, once you find some ratio of bale sizes that will keep the donkey from eating, an arbitrarily small change can get it to eat eventually.
Okay, sure, but that seems like the problem is “solved” (i.e. the donkey ends up eating hay instead of starving).
It can also use the “always eat the left bale first” strategy, although that gets kind of odd if it does it with a bale of size zero.
There is a problem if you want to make it make an actual binary decision, like go to one bale and stay.