tag:blogger.com,1999:blog-2237906900456925233.post7527539810368672912..comments2023-10-18T23:36:58.396+08:00Comments on 數學資料庫手記: 培正數學邀請賽:經典重溫(二)MathDBhttp://www.blogger.com/profile/18353093974880979999noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-2237906900456925233.post-24509612908619003712007-10-15T23:06:00.000+08:002007-10-15T23:06:00.000+08:00pop:Solution booklets are published every year. Th...pop:<BR/>Solution booklets are published every year. This year a combined version of the first five years' solutions will be published. We are therefore trying to include a variety of nice alternative solutions. To express gratitude for providing your alternative solution, we will give you a complimentary copy of the combined version which will be published by the end of the year. Would you mind sending an e-mail to pcimc.sol@gmail.com leaving your details?Kahoohttps://www.blogger.com/profile/04608296510896520430noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-90127038396083832042007-10-14T19:27:00.000+08:002007-10-14T19:27:00.000+08:00Kahoo, it's my pleasure.As i can only get the nume...Kahoo, it's my pleasure.<BR/><BR/>As i can only get the numerical solution from the net, that s why i work out my own.<BR/><BR/>So would you please let me know where i can download the offical detail solution?Pophttps://www.blogger.com/profile/17406316084081487132noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-24723257702200533442007-10-14T11:19:00.000+08:002007-10-14T11:19:00.000+08:00pop:Your solution is very nice, and it does not re...pop:<BR/>Your solution is very nice, and it does not require the observation that 66.6% is close to two-thirds. Would you mind letting your solution be included in a future version of the PCIMC solutions?Kahoohttps://www.blogger.com/profile/04608296510896520430noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-35143713152967597982007-10-08T17:10:00.000+08:002007-10-08T17:10:00.000+08:00Let n be the number of votes for Mr Tung, N be the...Let n be the number of votes for Mr Tung, N be the total number of votes<BR/><BR/>according to the question, <BR/>6655/10000 <= n/N < 6665/10000<BR/>2000n / 1331 >= N > 2000n / 1333<BR/>n + 669n/1331 >= N > n + 667n / 1333<BR/><BR/>N bounded by [n+ 667n/1333, n +669n/1331)<BR/>Now, find min. n such that the integral part of LHS and RHS are diff.<BR/><BR/>consider only 667n/1333 and 669n/1331<BR/><BR/>The remainder of 667n/1333 <BR/>for odd n (2m+1) = 667 + m --(1)<BR/>for even n (2m) = m --------(2)<BR/><BR/>The remainder of 669n/1331 <BR/>for odd n (2m+1) = 669 + 7m ---(3)<BR/>for even n (2m) = 7m ---------(4)<BR/><BR/>where m = 0, 1, 2, ...<BR/><BR/>clearly, (3) is growing faster with respect to n and lead to diff. integral part for LHS and RHS<BR/><BR/>Thus, <BR/>669 + 7m > 1331<BR/>m > 662 /7 = 94.57<BR/>therefore, min m = 95, i.e. min n = 2*95+1=191 <BR/>(N = 287)Pophttps://www.blogger.com/profile/17406316084081487132noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-48249791358389943982007-10-03T08:05:00.000+08:002007-10-03T08:05:00.000+08:00哈,記起來了。你不提起這情景,我也想不起這件事!哈,記起來了。<BR/><BR/>你不提起這情景,我也想不起這件事!Andy Chanhttps://www.blogger.com/profile/00595673356023147822noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-39295468074970397192007-10-01T21:19:00.000+08:002007-10-01T21:19:00.000+08:00Andy:你不記得了嗎?那是當年荃官的聯校活動上孔 sir 提出的,當時你也在場啊。不過他確實的做法...Andy:<BR/><BR/>你不記得了嗎?那是當年荃官的聯校活動上孔 sir 提出的,當時你也在場啊。<BR/><BR/>不過他確實的做法我也不太記得清楚,我一時間也找不到那一張筆記。他大概是在座標平面上畫了 y=0.6655x 和 y=0.6665x 兩條直線,然後用 Pick's formula 數格點的。Kahoohttps://www.blogger.com/profile/04608296510896520430noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-1315971244957860482007-10-01T16:28:00.000+08:002007-10-01T16:28:00.000+08:00Pick's Formula?願聞其詳。Pick's Formula?願聞其詳。Andy Chanhttps://www.blogger.com/profile/00595673356023147822noreply@blogger.com