tag:blogger.com,1999:blog-6213919025256134910.post8887603871668695785..comments2023-05-15T08:32:02.241-07:00Comments on The Math Contest: 2007: 17 and 25.Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6213919025256134910.post-48742881225719859342011-03-26T21:34:51.710-07:002011-03-26T21:34:51.710-07:00By gimmick I meant that once I rewrote it (yes, go...By gimmick I meant that once I rewrote it (yes, good log practice), I just guessed at an answer, and didn't worry about the existence of other possibilities.jd2718http://jd2718.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-6213919025256134910.post-58849933297958718062011-03-26T12:30:39.717-07:002011-03-26T12:30:39.717-07:00I don't know about calling 25 a gimmick. I lik...I don't know about calling 25 a gimmick. I like it for its solid use of prime bases that requires the kids to know their exponent rules.Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-6213919025256134910.post-62315655631692794932011-03-26T09:56:25.277-07:002011-03-26T09:56:25.277-07:0025 presents us with a gimmick - if they are asking...25 presents us with a gimmick - if they are asking for a value, they we don't necessarily need a general solution, just one specific set of a, b, c that makes the eqn true. We don't even have to worry about how many solutions there are - just find one, and done.<br><br>There is a clean dissection (I was surprised) for 17. Choose the rectangle with coordinates (1,7) (1,3) (4,3) and (4,7), extend from each vertex vertically or horizontally to a vertex of the polygon, and drop a perpendicular from (5,10). No need to calculate any points, and we have 4 right triangles and two rectangles.<br><br>Might be easier than the subtraction? (1 rectangle, 4 rt triangles, but subtraction is more prone to sloppy mistakes?) Still, I would subtract, because the cleanness of the cuts is not expected.<br><br>Jonathanjd2718http://jd2718.wordpress.com/noreply@blogger.com