| [ QuizWit ] in KIDS 글 쓴 이(By): iLUSiON (정 무경) 날 짜 (Date): 1994년06월28일(화) 12시14분20초 KDT 제 목(Title): RE:이지원 i have two different integers. both are greater than or equal to 2. there are two wise people named S and P. i give S the sum of the two numbers and P the product. so S only knows the sum of two numbers and P only knows the product of those. i let them talk to each other only once. S says to P first. " i have the sum only. so i envy you because you have the product. but you can't know those two numbers only from what you've got." P " ..... " (he thinks) " now i know them from what you said." S " ..... " (he thinks) " now i know them from what you said too." what are those numbers? solution: let S= a + b, P= a*b and let each statement be ST1, ST2, ST3. The smallest possible S = 11 since 11= 2 + 3*3 = 3 + 2*2*2 = 2*2 + 7 = 5 + 2*3 case (1) (2,9) P = 18 = 2*3^2 ST1 true, ST2 true because P thinks S must be one of 11, 9 but S can not be 9 because ....bla bla case (2) (3,8) P = 24 = 3^2^3 ST1 true ST2 true because P thinks S must be one of 10, 11, 14 case (3) (4,7) P = 28 = 7*2^2 ST1 true ST2 true because P thinks S must be one of 11, 16 case (4) (5,6) P = 30 = 2*3*5 ST1 true ST2 is false because P thinks S must be one of 11, 13, 17 and 17 can be partitioned into two numbers which are not primes. (5 distinct pairs) Now the hardest part is ST3. Hence the case (4) is out of the consideration. However for the remaining cases 1,2,3 , since they are all true for ST1, ST2 S can not know which case is the answer. Therefore, there is no solution for S<= 11. However, the next possible S = 17 and it generates 5 cases ..... therefore, this problem has no solution at all for S < 16. 17일경우는 너무 복잡합니다. 이상하군요. 분명 답이 S= 11경우에 나와야 할듯 싶은데 논리에 모순이 있는것으로 미루어 아이시스(발음이 맞아요?)님의 문제자체가 restriction이 허술한듯 싶군요. advanced problem: 아이시스님 문제 낑낑대다가 수학적으로 재미있는 파티션 문제를 발견했습니다. 쨔쟌... let Z(n) be the n-th natural number which can not be partitioned into two prime numbers.. 당연히 Z(1) = 2, Z(2) = 11, Z(3) = 17 인데요..그럼 일반항은 뭘까요? 물론 1도 프라임으로 쳤구요 첫항은 2부터 시작했습니다. 1이 아닌. ====== 환상 (TM) ====== 현재 읽고있는 책: Special Functions A Group Theoretic Approach( Lectures of Eugene P. Wigner) 음악: 조지윈스턴 셉템버, 쓰고있는글: 스넵틱디스오더환자에 대한 보고서, 게임: The Last Admiral, 풀고있는수학문제: n차원 parallelotope, 먹고있는것: 뻔데기통조림 |