tag:blogger.com,1999:blog-2400513859305780710.post3250747397323411063..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Yay! Putnam! Topic: Algebra/Polynomials. Level: AIME.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2400513859305780710.post-10069784583698297992006-12-03T15:25:27.000-08:002006-12-03T15:25:27.000-08:00you dont even need to find the coordinates, once y...you dont even need to find the coordinates, once you know one vertex is (-1,-1) and the other two lie on line y=1-x, you are done. since point (1/2,1/2) must be half way between the the unkown vertecies.<br><br>for the practice problem, substitude w^2 for x^2+y^2 and you get a circle, and its easy from there.<br><br>this year's putnam was weired.amirhtlusanoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-73958065822482388212006-12-03T15:29:55.000-08:002006-12-03T15:29:55.000-08:00funny thing, when i saw this problem (B1), since i...funny thing, <br>when i saw this problem (B1), since i had eaten lots of thai food for lunch, there was not much blood flow to my brain, so i spend like 20 mins and just screwed around and getting no where, <br>it was until i finished eating an orange, that my brain started working again, i did B2 and B3 first, before i realized how to do B1.<br><br>i highly recomend eating Oranges during putnam; who knows, maybe if i had eaten a box of oranges during usamo last year i would have won it....darn....<br><br>lol.amirhtlusanoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-68243479784263244502006-12-03T15:52:11.000-08:002006-12-03T15:52:11.000-08:00Well I figured that finding the points was the bes...Well I figured that finding the points was the best justification as to why only one equilateral triangle exists, though the argument can easily be proven rigorously in other ways as well I suppose.<br><br>Haha, I think B2 was easier than B1, because it was classic pigeonhole. B1 required a little intuitive factoring. I'll have a couple more Putnam problems here in the next couple of days =).paladin8noreply@blogger.com