Outerspace Outlaw
Alert! An outlaw has escaped from Planet D in the diagram. Every day, the outlaw moves to an adjacent planet which has an active link. He must move whenever possible, and which planet he moves to is entirely random.
The links (represented by grey lines between planets) are basically active all the time. But, in order to capture him, every day you can shut down any two links between any two planets for a day. You can shut down the same link as many times as you want. Ultimately, you must corner him into any planet by shutting down the links, isolating that planet. By now, the outlaw is either in Planet A or Planet E.
Is there a guaranteed way to catch the outlaw? If so, what is the fastest method? If not, is it completely impossible or is it completely luck-based?
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1 solution
It is doable in under a week - in fact, in 5 days.
The key is giving the outlaw as little different possibilities as possible. He is at A or E. We don’t want to risk the outlaw going anywhere further from B or D, because if the outlaw went to A, he’s bound to go to B or D. So, we’ll block of EH and EF.
Now we know the outlaw is in B or D. We don’t want the outlaw to return to E, as it has 4 paths. So, we’ll now block off BE and DE.
Now we know the outlaw is in A or C. It may seem like we aren’t getting anywhere - after all, he’s still either in one planet or another. But note that the amount of possibilities the outlaw can go to in his next turn is shrinking. From Day 1, he could go to B, D, F or H. From Day 2, he could go to A, C, or E.
Now, he can only go to B, D or F. We’ll block AD and CF, so he has to go to B.
From here, it should be pretty obvious what to do. I moved him to A, but you can easily do it with C.
As I mentioned earlier, what we were doing was scaling down his options with every move. Note that E and F connect to four other planets, B and I connect to three, and A, C, D, G, H and J connect only to two.