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Comment by margalabargala | Hacker News Reader

I certainly would have, had I suggested the problem trivial! I'll keep that in mind for if I suggest things are trivial rather than suggesting I lack understanding.

> You also can't generally "and so on" constrained combinatorial arrangements like this.

I know you can't generally but in the specific case I proposed you can (3 sets of 3, 4 sets of 4, 5 sets of 5, each dice taking one ordinal of each set).

You might want to check that your proposed generalization criticism applies to the generalization at all before suggesting the arrangement doesn't work :)

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Didn’t they do the exact opposite of suggesting the problem was trivial?

You're saying you knew the thing you wrote for n=3 specifically was wrong and just wanted someone else to confirm? I don't know man, I'm not really buying it. I think you did the classic dismissive nerd thing[1] and hedged it like this for plausible deniability.

I don't get the gotcha you're trying to do. Yes, the simple pattern you posted can be extended, but it has very little to do with the problem. If you had suggested [1,2,3] [4,5,6] [7,8,9] worked I would still have made my comment; I think the fact that you found a pattern that could be extended easily should have itself been a counter-indicator. Compare with something like the Fano plane[2].

I would want you to take away from this that posting the thing you came up with in "20 seconds" isn't as neutral a contribution to conversation as you thought. Things are often complicated and worth engaging with. It would have been cool if you kept going far enough to see there's a nice argument that it's actually impossible to solve it with n-sided dice for n people if n>2.

[1] https://xkcd.com/793/ [2] https://en.wikipedia.org/wiki/Combinatorial_design

Do you think the dismissive nerd thing is, like, a goal people set out to do?

You seem to have spent your time around sufficiently many unpleasant people that you see their behavior everywhere, even when explicitly corrected. I'm sorry for that.

Could I have independently gone through and rigorously deconstructed my solution? Sure, and we would all be poorer for it. See, there's another, valuable reason people say what I said beside the "classic dismissive nerd thing".

For every person with a question, there's probably 5 more with the same question who didn't ask. By writing down questions like I did, and inviting their answer to be written down, that provides education not only to me but to anyone who reads it after having similar thought.

I consider that sufficiently valuable to create, that I am willing to accept a handful of people criticizing me for "doing the dismissive nerd thing".

So yes. I knew the thing I wrote was wrong, I didn't know why/how, and I wrote it down as is rather than just going off on a personal side quest to come up with some generalized proof. And I would do it again.

Ha, I guess we just see the world differently. What you're describing sounds exactly like the dismissiveness I'm talking about.

I hope your life is full of "personal side quests" pursuing questions that appeal to your particular sensibilities. You should wrestle with that feeling of not understanding something, use it as a signpost pointing towards interesting ideas rather than as a reason to stop.

I'll get you started on the proof: Suppose for n>2 you have n n-sided dice with disjoint sets of numbers and you want each of them to have an equal chance of rolling the highest number. One of them must have the highest overall number, and it will roll that 1/n of the time. What can you say about the other numbers?

The relative ordering of the other dice doesn't depend on this result. They need to each have an equal chance of coming first. How many total outcomes are there?

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