Putnam

[norsenerd]

Here is what the Putnam is for those of you who don't know: It's a national math competition that only the best mathamatics undergraduates take. It's held once a year every year on the first saturday in December (today) It's held in two three hour blocks sperated by two hours. 12 questions 6 in the morning and 6 in hte eavning. Each question worth 10 points. Median score is 0 a-lot of years.<br><br>I just got thorugh taking it. I think I got 3 right and put enough down on a few others to get some partial credit. Thus I think I scored in the mid to upper 30's when I was expecting a 0 (just because that's what one should expect). I can give some of the questions latter if you want. The ones I got corectly are the folowing:<br><br>Given a_1, a_2, ... , a_n and b_1,b_2, ... b_n are non negative integers show that:<br><br>(a_1*a_2*...*a_n)^(1/n)+(b_1*b_2*...*b_n)^(1/n)=<((a_1+b_1)*(a_2+b_2)* ... *(a_n+b_2))^(1/n)<br><br><br><br>Can there exist polynomial functions a(x), b(x), c(y), and d(y) such that<br><br> 1+x*y+x^2 *y^2= a(x)*c(y)+b(x)*d(y)<br><br>for all x,y.<br><br><br><br><br>Given that f(x) is a real valued funtion on the interval [0,1] show that:<br><br>the double integral form 0 to 1 from 0 to 1 of the absolute value of (f(x)+f(y)) dxdy is greater then or equal to the integral from 0 to 1 of the absolute value of (f(x)) dx.

[Tavis]

Ooh.. math.. This will be just as much fun as clip finding. <!--emo&:)--><img src='http://definecynical.mancubus.net/forum ... /smile.gif' border='0' style='vertical-align:middle' alt='smile.gif' /><!--endemo--> <br><br>*is rather distracted, but will attempt them tonight*

[Supersmoke]

Is it multiple choice?

[norsenerd]

<!--QuoteBegin--> <table border='0' align='center' width='95%' ><tr><td class='quotetop'><b>Quote:</b> </td></tr><tr><td class='quotebody'> Is it multiple choice?<!--QuoteEnd--></td></tr></table> <!--QuoteEEnd--><br><br><br>*Laughs* Right *rolls eyes*

[Zylo]

Wow. I'm gonna print these out and show them to my Pre-Calc teacher and see if he knows how to do them. I bet he can't; he can't teach in general.

[penguinita]

<!--QuoteBegin-norsenerd+Dec 7 2003, 10:04 AM--> <table border='0' align='center' width='95%' ><tr><td class='quotetop'><b>Quote:</b> (norsenerd @ Dec 7 2003, 10:04 AM)</td></tr><tr><td class='quotebody'> I can give some of the questions latter if you want. <!--QuoteEnd--> </td></tr></table> <!--QuoteEEnd--><br> first- congrats on the 30-ish score!<br>second, i confuzed: do you mean you'll state more questions? (which i'd be intressted in) or that you'll post the answeres? (which i think woudl be best in another thread s.t. we can't see them acidentally) <br>

[Burning Sheep Productions]

<!--QuoteBegin-norsenerd+Dec 7 2003, 10:04 AM--> <table border='0' align='center' width='95%' ><tr><td class='quotetop'><b>Quote:</b> (norsenerd @ Dec 7 2003, 10:04 AM)</td></tr><tr><td class='quotebody'> (a_1*a_2*...*a_n)^(1/n)+(b_1*b_2*...*b_n)^(1/n)=<((a_1+b_1)*(a_2+b_2)* ... *(a_n+b_2))^(1/n) <!--QuoteEnd--> </td></tr></table> <!--QuoteEEnd--><br> Ah-Buh?<br><br>*Collapses*

[Zaaphod]

Ouch, it hurtss uss, nassty norssenerd. <!--emo&:blink:--><img src='http://definecynical.mancubus.net/forum ... /blink.gif' border='0' style='vertical-align:middle' alt='blink.gif' /><!--endemo--> <br><br>Sorry, my higher-level math skills have atrophied over the years. I was good in it once. Last century.<br>

[norsenerd]

<!--QuoteBegin--> <table border='0' align='center' width='95%' ><tr><td class='quotetop'><b>Quote:</b> </td></tr><tr><td class='quotebody'> Wow. I'm gonna print these out and show them to my Pre-Calc teacher and see if he knows how to do them. I bet he can't; he can't teach in general.<!--QuoteEnd--></td></tr></table> <!--QuoteEEnd--><br><br>*Laughs prety heavaly* You're right. I bet he won't.<br><br><!--QuoteBegin--> <table border='0' align='center' width='95%' ><tr><td class='quotetop'><b>Quote:</b> </td></tr><tr><td class='quotebody'> second, i confuzed: do you mean you'll state more questions? (which i'd be intressted in) or that you'll post the answeres? (which i think woudl be best in another thread s.t. we can't see them acidentally) <!--QuoteEnd--></td></tr></table> <!--QuoteEEnd--><br><br>both probably. Although befor I look at the answers I can only give you 3.

[Tavis]

I printed it out but then ignored them because I was distracted from chat and here... Ack. Y'know, that discussion about mathematics and physics was very refreshing, and I know that it's going to drive everyone nuts now that we both got started on the subject. <!--emo&:D--><img src='http://definecynical.mancubus.net/forum ... iggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo--><br><br><br>EDIT: Of course, I meant "All", not "both".. Sorry.

[penguinita]

both? i thought there were three of us involved? <!--emo&:)--><img src='http://definecynical.mancubus.net/forum ... /smile.gif' border='0' style='vertical-align:middle' alt='smile.gif' /><!--endemo-->

[simon]

Maths....in my BRAAIN! Holidays...NOT OVER!! AHHHHHHHHHHHHHHHHHhhhhhhhhhhhhhhhhhhhhhhhhh..............

[norsenerd]

Ok. three more problems today:<br><br>For intergars a,b,c,d,e let a*z^4+b*z^3+c*z^2+d*z+e = a*(z-r_1)*(z-r_2)*(z-r_3)*(z-r_4) for all z when a !=0. Fiven that r_1+r_2 is rational and that r_1+r_2 != r_3+r_4 prove that r_1*r_2 is rational.<br><br><br>For any positive integers interger n, how meny ways can you write down n as the sum of integers a_1 though a_n (i.e. a_1+a_2+ ... +a_n) such that a_1=<a_2=< ... =<a_n=<a_1+1. For example 4 can be writen 4 ways. 1+1+1+1 , 1+1+2, 2+2, 4.<br><br><br><br>What is the minimum value of the absolute value of (sin x + cos x + tan x + cot x + sec x + csc x) for all x?<br><br><br>Good luck!

[Burning Sheep Productions]

If I were taking that test, they'd think rutabegas were some kind of trend now.

[Supersmoke]

If it was a standardized test with the bubbled answer sheet, I'd make designs with the bubbles. I have no idea how to do that kind of math, and just thinking about it makes me want to rip my eyes out of my head.