Putnam

norsenerd · Postby **norsenerd** » Mon Dec 08, 2003 2:26 pm

OK. That said 3 more quesstions: If you have three points A, B, and C equaldistant on the circonferance of a circle of unit lenght centered at O show that if there is a point P placed in the interior of the circle and a being the lenght of the linesegment form A to P, b being the lenght of the linesegment form B to P, and c being the lenght of the linesegment form C to P that there exists a triangle of side length a, b, and c and that the area of this triangle only depends on the distance from P to O. If for real numbers a, b, c, A, B, and C with a!=0 and A!=0 prove that if the absolute value of (a*x^2+b*x+c)=<the absolute value of (A*x^2+B*x+C) holds for all x then the absolute value of (b^2-4*a*c)=<the absolute value of (B^2-4*A*C) holds for all x. Let S be the set of all non-negative integers. Let r_s(n) bet the set of all ordred pais (s_1,s_2) such that s_1and s_2 each lie in S, s_1+s_2=n, and s_1!=s_2 for all n in S. Can S be partitioned into two sets A and B such that r_a(n)=r_b(n) for all n in S?

Burning Sheep Productions · Postby **Burning Sheep Productions** » Tue Dec 09, 2003 12:50 pm

He he! I makes me think of killing people with guns!! Weee!

Msj · Postby **Msj** » Tue Dec 09, 2003 1:33 pm

Sorry I have NO idea *is stupid* <img src='http://definecynical.mancubus.net/forum ... /wacko.gif' border='0' style='vertical-align:middle' alt='wacko.gif' />

norsenerd · Postby **norsenerd** » Tue Dec 09, 2003 2:35 pm

<table border='0' align='center' width='95%' ><tr><td class='quotetop'>Quote: </td></tr><tr><td class='quotebody'> Sorry I have NO idea *is stupid* <img src='http://definecynical.mancubus.net/forum ... /wacko.gif' border='0' style='vertical-align:middle' alt='wacko.gif' /> </td></tr></table>  You're not stupid for not getting these. There are people in graduate level math courses that can't get these. There are even some Doctors n math who can't get these. These are very hard problems and it's a special skill to be abl;e to solve these problems in a short amount of time (yes 6 hours is a short amout of time to solve these 12 problems). Just because you can't do it dons't meen there's anythign wrong with your mathamatical capability. Also it says even less about your ability in other areas. You're not stiupid. If you were I wouldn't talk to you. Two more prolbmes (I can't exactly remember the last one) A diyke n-path is a path having n steps up (+1,+1) and n steps down (+1,-1) starting and ending at the x axis and never going below the x axsis. The number of down paths is the number of consecutive paths ending at the x-axsis. |............. |.........../.\. |...../.\./.....\..... (it's not putting my spaces in there. Tavis help!) |_./_______\./_\._______________ (x-axis) [Moderator's note: Non-breaking spaces didn't work, so I'm using periods. Sorry. This is tricky!] For example this diyke 5 paht has two down paths one of length 3 and one of length 1. Prove that for any fixed n there is a one to one corispondance between the diyke n-paths with only odd down pahts and the diyke n-1-paths. Take the n sequance 1, 1/2 , 1/3, 1/4, ... 1/n. Average each term with the one nexxt to it to get the n-1 sequance 3/4 , 5/12 , 7/24 , ... , (2*n-1)/(2*n*(n-1)) Keep doing this until you get a number a_n. Proove that a_n<2/n for a positive integers n.

Msj · Postby **Msj** » Tue Dec 09, 2003 2:47 pm

Do you know how to do them <img src='http://definecynical.mancubus.net/forum ... tongue.gif' border='0' style='vertical-align:middle' alt='tongue.gif' />

norsenerd · Postby **norsenerd** » Tue Dec 09, 2003 4:36 pm

I can do three. Like I said. If you can do one then you can do better then most of the people who take it. Seroisly. I can answer 3 or 4 more but I can't prove that the answers are corect so therefore that dosn't count.

Softpaw · Postby **Softpaw** » Tue Dec 09, 2003 8:00 pm

Ick, I despise mathematical proofs. Why can't they just believe that the answer is correct? What happened to "innocent until proven guilty"? You shouldn't have to prove your answer until someone proves it wrong. I didn't do well in Geometry at my high school <img src='http://definecynical.mancubus.net/forum ... iggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' />

norsenerd · Postby **norsenerd** » Tue Dec 09, 2003 8:03 pm

You're forgiting: Math is not a democracy. That's a very important concept. Justace works diferently: you're worng until proven right.

Softpaw · Postby **Softpaw** » Tue Dec 09, 2003 8:05 pm

There should be a revolution!!!!

Sabre · Postby **Sabre** » Tue Dec 09, 2003 8:34 pm

Methinks me brain is broken. <img src='http://definecynical.mancubus.net/forum ... /blink.gif' border='0' style='vertical-align:middle' alt='blink.gif' />

penguinita · Postby **penguinita** » Tue Dec 09, 2003 8:39 pm

felix- tahts' an awesome idea! i'm gonna hafta try 'innoncent until proven guilty' the next time i have no clue on a math proof. i did just end a proof last week with 'and i leave the rest of the proof as an excersize to the grader' and the grader didn't write anything next to it! (i actually got full credit, because i said at the start of the proof that there were 2 parts of the proof, and the second part could be proven similarly to the first part, and i proved the first part correctly.) but still, it was quite diappointing. i wanted a reaction from the grader!

norsenerd · Postby **norsenerd** » Tue Dec 09, 2003 10:46 pm

<table border='0' align='center' width='95%' ><tr><td class='quotetop'>Quote: </td></tr><tr><td class='quotebody'> |............. |.........../.\. |...../.\./.....\..... (it's not putting my spaces in there. Tavis help!) |_./_______\./_\._______________ (x-axis) [Moderator's note: Non-breaking spaces didn't work, so I'm using periods. Sorry. This is tricky!]</td></tr></table>  lol. interesting. I hope everyone gets the point. Good job though.

Phoxphyre · Postby **Phoxphyre** » Wed Dec 10, 2003 12:56 am

I GOTS TEH A ON ME GEMOTRY TEST!

erikbarrett · Postby **erikbarrett** » Wed Dec 10, 2003 6:16 pm

One quick question Norsenerd: you stated a few times a !=0. I have no idea how a factorial is equal to zero, (since 0! = 1 by definition) so I'll assume you meant "not a=0" (ie. a doesn't equal zero) PS. I responded to the first question. Was I close?

norsenerd · Postby **norsenerd** » Wed Dec 10, 2003 8:45 pm

First "!=" means does not equal. Thank Fox Chiled for pointing this out in an earlier theraed. It saves on typing. thus a !=0 means a does not equal 0 wheras if I put a! = 0 I would mean a factorial does not equal 0 which is not in the range of factorial.

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