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Problem 311
Posted: Sun Nov 21, 2010 7:28 pm
by wrongrook
Are quadrilaterals distinct if:
1) Side lengths are different?
2) Angles are different?
3) Both side lengths and angles are different? (my initial assumption)
I've tried computing B(10,000) for each of these but none of them match the answer given (cases 2 and 3 give answers too high, and 1 gives an answer too low).
It would help my debugging to know which case I should be trying to solve, but I am quite happy if people want to wait until the top 20 list is filled before answering this question.
Re: Problem 311
Posted: Sun Nov 21, 2010 8:04 pm
by TripleM
I haven't solved the problem, but I've reproduced the answers for the two smaller test cases, and it's what you'd expect: two quadrilaterals are identical if they share the same sides and the same angles.
Re: Problem 311
Posted: Sun Nov 21, 2010 9:08 pm
by wrongrook
Thank you very much, that was very helpful.
I get the correct answer now (for B(10,000) and B(1,000,000) at any rate), (I'd missed the C0<=B0 inequality, whoops)
Re: Problem 311
Posted: Mon Nov 22, 2010 6:06 pm
by RandyShane
Ugh. I'm one off for B(10000) and 121 off for B(1000000).
I think I'd rather be way off rather than 1 off, myself.
Re: Problem 311
Posted: Mon Nov 22, 2010 10:23 pm
by wrongrook
I think the problem setters were trying to give a hint by choosing N=10000 rather than some other value; I would recommend careful examination of N=10000 and N=5000.
Re: Problem 311
Posted: Tue Nov 23, 2010 6:11 pm
by rayfil
I'm one off for ...
That is not very informative. If you get one too many, it could be due to a very different cause as compared to being short by one.
Re: Problem 311
Posted: Tue Nov 23, 2010 6:31 pm
by RandyShane
rayfil wrote:I'm one off for ...
That is not very informative. If you get one too many, it could be due to a very different cause as compared to being short by one.
True.
My program is one short for B(10000) and 121 short for B(1000000).
Re: Problem 311
Posted: Wed Nov 24, 2010 12:19 am
by jaap
RandyShane wrote:My program is one short for B(10000) and 121 short for B(1000000).
Did you miss out the cases where CO = BO ?
If I do that I am 1 and 131 short on the example values.