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anyone doing it? how did you do? i dont think we can talk about answers yet though.

By Firebird12637 (Firebird12637) on Saturday, October 04, 2003 - 06:08 pm: Edit

yes, answered all 5, pretty easy questions...probly will get harder tho

By Fairyofwind (Fairyofwind) on Saturday, October 04, 2003 - 08:11 pm: Edit

Yes same here. Very easy. I'll post a pdf with my LATEX solutions monday morning.

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 01:34 pm: Edit

do u have a awebsite?

By Fairyofwind (Fairyofwind) on Sunday, October 05, 2003 - 09:10 pm: Edit

Yea. Not sure if okay to post solutions publicly yet

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 09:29 pm: Edit

should be. i dont know what kind of person has not mailed/faxed it... the deadline was saturday. Especially since not many people here seem to be doing the contest...

What's your website? im curious to see it.

i handwrote mine, so i cant really post them. they're nothing special anyways...

By Fairyofwind (Fairyofwind) on Sunday, October 05, 2003 - 09:44 pm: Edit

http://68.38.137.202/round1.pdf

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 09:55 pm: Edit

were we supposed to explain how to go about arranging the triangular #'s in a circle? I didnt...

Those are nice, by the way. What's your website for? All i saw was another math solution, then some mp3.

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 10:01 pm: Edit

correct me if im wrong, but i thought you only put some ending to the proof, e.g QED, W^5, for non-numerical proofs. That's what i've always done, seems kind of different to me to do it for when we're just trying to find a numerical answer.

By Fairyofwind (Fairyofwind) on Sunday, October 05, 2003 - 10:04 pm: Edit

Yes, it's awkward but I suppose it is tacitly understood for example, in #5, that the theorem to be proved is "EF=260." Lol as for #3... I suppose they can't really demand that you show how you arrived at your answer, so it's all right. It's like my #4, the 3*2^n-1 is obviously very artificial, I don't show how I got that conjecture in the first place, but it doesn't matter.

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 10:10 pm: Edit

well, those are very nice. i bet some will be posted on the website, and at the very least, commended.

By Jimjunior (Jimjunior) on Sunday, October 05, 2003 - 10:51 pm: Edit

I used the same methods for everything but #2 and got the all teh same solutions. What program did you use for those solutions? They make my handwritten ones look a bit amateur

By Fairyofwind (Fairyofwind) on Sunday, October 05, 2003 - 10:54 pm: Edit

What did you do for #2? I'm using LaTeX. Here's the source code http://68.38.137.202/round1.tex

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 11:10 pm: Edit

n^5-1 = 6p
(n-1)(n^4+n^3+n^2+n+1)=6p, (i think), equate factors.

Jim, did you get his expression for the game theory one (i forget the #) 3*n^2-1? i did not, i just explained how to go about getting the #'s

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 11:11 pm: Edit

Most people handwrite or type, but they dont usually TeX their solutions...it's a lot of time + most people (including me) dont know how to use it yet. I hope to learn sometime this year though if i get the time.

By Fairyofwind (Fairyofwind) on Sunday, October 05, 2003 - 11:21 pm: Edit

I'm eagerly awaiting the geometric construction problem that occurs each year that I won't be able to do.... =\ (or some fractal problem, or some problem like year 14 round 1 #1 with the stupid building sides, that's not math). Pfft.

By Billiam2 (Billiam2) on Sunday, October 05, 2003 - 11:25 pm: Edit

i actually got that one wrong.

I got the fractal one though. Did you try that one?

By Fairyofwind (Fairyofwind) on Sunday, October 05, 2003 - 11:30 pm: Edit

This is my first year doing the USAMTS (one reason was that I was discouraged by the building sides problem). But I liked the limit solution for that fractal problem.

By Jimjunior (Jimjunior) on Monday, October 06, 2003 - 07:47 pm: Edit

For number two I proved that 6p was the product of two numbers greaters than 6. It follows that 6p has at least two prime factors other than 2 and 3 and cannot be prime.

I didn't use the equation for the game problem, although in solving it, I saw the pattern. I used words to justify the strategy then listed the winning numbers less than 2003.