Problem 233

SmuK · Post by **SmuK** » Fri Mar 20, 2009 10:15 am

Can someone confirm these results for Problem 233 (View Problem)?

Some random values of N such that f(N) = 420: 1328125, 84246500, 248431625.
My code compute approx 10^7 such numbers <= 10^11.

Thanks in advance.

Tommy137 · Post by **Tommy137** » Fri Mar 20, 2009 10:45 am

SmuK wrote:Some random values of N such that f(N) = 420: 1328125, 84246500, 248431625.

f(1328125) = 180

f(84246500) = f(248431625) = 420

SmuK · Post by **SmuK** » Fri Mar 20, 2009 3:34 pm

"Congratulations, the answer you gave to problem 233 is correct."

Thanks a lot. It was a stupid bug

hisoka-san · Post by **hisoka-san** » Mon Apr 20, 2009 6:25 pm

My code returns 30875234922 for n<=38000000, is it correct?

daniel.is.fischer · Post by **daniel.is.fischer** » Mon Apr 20, 2009 6:40 pm

quintana · Post by **quintana** » Mon Apr 27, 2009 4:27 pm

for n<=10^10 i have 2709499279563106.
is it correct?

Tommy137 · Post by **Tommy137** » Mon Apr 27, 2009 4:49 pm

quintana wrote:for n<=10^10 i have 2709499279563106.
is it correct?

Unfortunately, it's not.

You aren't the first one to get this particular result, though.

quintana · Post by **quintana** » Mon Apr 27, 2009 4:52 pm

it's interesting because i have correct answer for 38000000. thanks!

quilan · Post by **quilan** » Tue Apr 28, 2009 7:25 pm

Yeah, you're on the right track, but are missing something that a lot of other people missed initially too.

Tommy137 · Post by **Tommy137** » Wed Apr 29, 2009 7:32 pm

quintana wrote:it's interesting because i have correct answer for 38000000. thanks!

It seems you got it now

Congratulations!

quintana · Post by **quintana** » Thu Apr 30, 2009 6:31 pm

thanks, i got it allright! i got the idea long time ago, but like p180 this one had a catch beyond idea. again, forum was very helpfull.

hendrikS · Post by **hendrikS** » Sun Jun 07, 2009 12:07 am

Just a quick question for clarification:

"sum of the integers": Does it mean sum of the coordinates, that are integers up to 10^11? And if so: X or Y

rayfil · Post by **rayfil** » Sun Jun 07, 2009 3:34 am

What is the sum of all positive integers N

The actual value of the other integer coordinates on the circles are immaterial. Look at the definition given for f(N).

thundre · Post by **thundre** » Wed Aug 24, 2011 3:50 pm

quilan wrote:Yeah, you're on the right track, but are missing something that a lot of other people missed initially too.

I have an elegant algorithm that gives the same wrong results for 1e10, 1e11 and the correct one for 38e6. I don't see any way it could be double-counting solutions.

Now I'm running a brute-force check counting down from 1e10 to see where it's making the mistake. It's taking forever. AAARGH! Would it help if I pull my hair out?

Seriously, this isn't something dumb like an overflow bug, is it?

update: Got it! It wasn't an overflow bug, I just had to look a little deeper into the characteristics of f().

ffff0 · Post by **ffff0** » Wed Sep 28, 2011 8:12 am

Same as everyone. As for now, i can't see any difference for even and odd N. And i can't understand why answer for 38000000 is correct and answer for 10^11 is not. I simply don't see any special cases between this numbers.

My code finds 5422051 solutions for 10^11. Is it too big or too small?

Update: Wait a bit, I've got an idea.

Update 2: And hero have won once again without any help!
There are 5422629 solutions in total and there is no difference between even and odd N. It's something else.

amidar1 · Post by **amidar1** » Tue Dec 20, 2011 12:41 am

The subject of N <= 10^10 came up, but without a definitive response. Can anyone tell me if the correct answer for 10^10 is...

2709680426923506

It's very close to what quintana had, but not quite the same.
I'm getting the right answer for N <= 38 million (though I'm not sure what was special about the number 38 million), but evidently not the right answer for N <= 10^11, and it's driving me a little nuts.

Thanks!

ffff0 · Post by **ffff0** » Tue Dec 20, 2011 3:36 am

Sorry, it's too small.

amidar1 · Post by **amidar1** » Tue Dec 20, 2011 12:34 pm

Sorry, small bug.

for N <= 10^10: 2710041165705856 ?

EDIT:
Nevermind! Introduced another small bug while fixing the first. Now they're both fixed!

TheEvil · Post by **TheEvil** » Thu Dec 29, 2011 5:43 pm

Thank you for all the very helpful comments on this question. It helped me a lot when I saw a lot of other people missed one little thing. After I found that I felt I should give my diploma back.

So far one of the best problems I solved, even if it took me three days to solve it, but it worth.

snapey1979 · Post by **snapey1979** » Thu Mar 01, 2012 1:17 pm

Thanks to all posters above. I have to say that the open forum was great for this one - thanks for giving a sample answer for the problem on toy scale. When I realised my answer for 38000000 was wrong, i went hunting...

Helped me find a stupid bug using a less than instead of less than equals!!!! I'd had the code right since first writing it but for this bug!

Probably the hardest one I solved so far. Got the idea quite quickly, but debugging was a nightmare.

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