Problem 241

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genious999
Posts: 53
Joined: Mon Oct 20, 2008 10:48 pm

Re: Problem 241

Post by genious999 »

I haven't done this problem yet, and have no idea how, but 10^9 should not be difficult to brute force, so I don't see a real need for such a hint.

sinan
Posts: 16
Joined: Mon Sep 15, 2008 10:14 am

Re: Problem 241

Post by sinan »

Yes this one seems to be a hard one but there are 10 to 20 problems I spent more time to solve than this one.

I had found an effective algo on the first day. I even tried to do it by hand (later I checked that I had found 50% of the numbers by hand) then I switched to coding which took most of my time until I solved it.

helstreak
Posts: 19
Joined: Mon Jan 26, 2009 5:00 am

Re: Problem 241

Post by helstreak »

Just wondering, how many k+1/2 numbers are below the 10^18 limit? I've been able to find 15...

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daniel.is.fischer
Posts: 2400
Joined: Sun Sep 02, 2007 11:15 pm
Location: Bremen, Germany

Re: Problem 241

Post by daniel.is.fischer »

Too few.
Il faut respecter la montagne -- c'est pourquoi les gypaètes sont là.

helstreak
Posts: 19
Joined: Mon Jan 26, 2009 5:00 am

Re: Problem 241

Post by helstreak »

I know that's too few, that's why i'm asking how many there are hehehe :)

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daniel.is.fischer
Posts: 2400
Joined: Sun Sep 02, 2007 11:15 pm
Location: Bremen, Germany

Re: Problem 241

Post by daniel.is.fischer »

Okay, so then: in absolute numbers, you've not missed many, the percentage of those you missed is significant, though.
Il faut respecter la montagne -- c'est pourquoi les gypaètes sont là.

nrajsaxena
Posts: 3
Joined: Sun Mar 22, 2009 3:54 am

Re: Problem 241

Post by nrajsaxena »

I have so far found 21 such numbers < 10^18 using manual search (of course guided by a selection algorithm using Sage). Also my manual selection algorithm stumbled on few that exceeded 10^18. I believe I know the algorithm but I suspect it is a bit awkward to march through the multipliers. Now I am writing the algorithm to make sure if I have missed some. I suspect I am not that far off from the actual numbers that are less than 10^18 and produce k + 1/2

hisoka-san
Posts: 20
Joined: Sun Jan 25, 2009 6:14 pm

Re: Problem 241

Post by hisoka-san »

In my opinion this problem is not as hard as many people think (judging by the number of solvers..)

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