In post 238, biancospino wrote: Eh, let's do one.
Suppose there's a plane with 400 seats; all seats are booked, and all passengers are actually going to take the plane.
Passengers board the plane in a random order. The first one sits on the wrong seat (that is, a seat different from the one indicated in their ticket); all subsequent passengers sit on the correct seat if it's not occupied by someone else, and on a random unoccupied seat otherwise.
What is the chance that the last passenger to board will sit on the correct seat?
Math and Logic Puzzles: Redux
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Spoiler:-
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Perfect!
Whoops - the answer is I wrote the question at 2 am and didn't realise you'd need to compute Q(n) for general p to get this part. I don't know if there's a nice formula for it (:In post 243, biancospino wrote: But atm idk how to compute Q(n) nicely for general p.-
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Yeahhh not sure what there is to say exceptwhat is the?? Sorry if you wasted any time on that.hypergeometric function
Here is another one.
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Both the answers look good to me ^^.
I was asking if these sets in were finite in general, without the constraint they have to have 2023 elements, but I think bianco's answer is also correct.-
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I haven't forgotten about this, just haven't sat down to crack it yet. But also anyone else feel free to give it a try!-
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How this went:
I looked at your first hint and was like "ok! This seems pretty helpful".
Couldn't solve the problem.
Then I looked at your second hint and was like "hmm thisliterallytells me the construction I need to solve this, there's no way I don't solve this now".
Still couldn't solve it.
Then I looked at your very heavy hint and thought "ok I went too far, this literally says what the solution is, should have stuck it out with two hints. Ah well, whatever, I should be able to construct a proof now".
But Istillcouldn't find the optimal strategy!!
Then I asked my friends Google and Wikipedia who finally helped me with the optimal strategy
Spoiler: The wikipedia article
Ok so the solution is that
Spoiler:
but the hints and wikipedia definitely did all the heavy lifting-
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I'm out of fun maths problems I can name off the top of my head but I can probably dig something out if there's interest
Also to say that Isolvedbianco's problem would be, uh, very very generous so I feel like it's still open to attempts that don't consult Wikipedia-
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Yeah it's not really your fault, lolIn post 258, biancospino wrote: This is correct.
Sorry for spoiling it for you (thou proving the Very Heavy Hint was much of the difficulty anyway, so you really spoiled yourself a bit there...)-
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Spoiler: Explanation of what an "increasing subsequence" is
I think this may be a slightly harder problem that the other two I shared. But apparently there are "multiple proofs", maybe there's a really nice way of framing it that makes it simple!Last edited by Aisa on Fri Apr 14, 2023 6:57 am, edited 1 time in total.-
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Very neat.
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Spoiler: sudoku
I will continue to edit this until either I finish it or I get home
I got home first. Maybe I will finish this tomorrow. Maybe it will be incomplete forever.
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