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Comment by RiderOfGiraffes | Hacker News Reader

I don't understand your objection ...

    > ... it depended on something not stated in the
    > problem; in brief it requires multiple interdependent
    > participants to adhere to a pre-agreed algorithm
    > for searching a data structure whose topology
    > they cannot know in advance.

It clearly says:

    The prisoners have a chance to plot their strategy in advance

That seems pretty clear: the prisoners must pre-agree a strategy to do what they're going to do. Not adhereing to that seems to follow naturally.

What am I missing?

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Quite correct. But when I was imagining it, I began thinking of different ways to 'line up' the boxes and it's not clear to me from the problem statement that the layout is predictable in advance. See below for why (I think) a circular arrangement would defeat the strategy. Lines can be curved, and curves may be closed.

Lines are a special type of curve - a straight curve. This precise and simple mathematical definition precludes such confusion.

Can't argue with that. I guess I'm thinking of those puzzles that say things like 'can you draw a line that passes through all these points', and when you can't, the answer turns out to be that it's not a straight line. I'll leave my wrong arguments up for educational purposes :-)

Ah, so what I'm missing is that you think the boxes may be arranged in other than a straight line.

Your reference to topology confused me. I thought you were referring to the topology of the cyclic structure(s) induced by the permutation, not to the geometry of the physical arrangement of the boxes.

Now I understand, but I still think theproblem statement is clear.

It's not clear that they can distinguish the boxes in advance, but apart from that, I think it's perfectly clear.

> I think it's perfectly clear.

The problem as stated, or the objection in the HN comment 835216?

I think the problem as stated is perfectly clear, and I thought that when I first met it a few years ago. It boggled me then that it was possible, and it continues to boggle me somewhat even now.

I agree with you that the problem as stated is perfectly clear. I thought the statement lacked a little clarity about how distinguishable the boxes were for the prisoners that haven't seen them before, but on second reading I think that's clear too.

I also heard about it a few years ago, and discovering the solution was mind-blowing! It's stunning that it's possible.

If you're a fan of these types of puzzles please check out my contribution to the field:

http://www.srcf.ucam.org/~te233/maths/puzzles/evenharder.htm...

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