| [ QuizWit ] in KIDS 글 쓴 이(By): guest (l'hiver) <Poincare.Math.M> 날 짜 (Date): 1998년 11월 15일 일요일 오전 08시 05분 55초 제 목(Title): [insight] ruler problem oh after all this years, finally pomp gave us very interesting problem which is nothing to do with NUMBER THINGS! i have thank pump for pumping up some intellectual stimulation. your generalization to 7n+15 is infact 7(n+2) + 1. what does it mean? it means your generalization is ok for 1 mod 7. so now the question is what if x mod 7 where x is other than 1? ^^ the next question we have to ponder is pomp's general solution to 1 mod 7 case. can we prove it is infact minimum without running computers ? it is a side remark but if you can use the ruler as many times as you want, the answer is trivial. the following set of intergers represent any intergers uniquelly. {1,p_1,p_1*p_2, ..... , p1*p_2*...p_n, ....} for any ingegers p_1 <= p_2 <= p_3 ... this representation is optimal in certain sense and equivalent to coin exchange and knap-sack problem. in fact this representation is the ONLY representation of integers. from integers, you go to Q and R. ^^ now i do i prove the POMP's problem with this side remark? again trivial. my obove ruler will measue anything if the ruler is used as many times as i want. if you want to measuer 2 cm you must use ruler 2 times if p_1 is not 2. using ruler m times is equivalent to m linear transformation. infact translation. if x = (a_1,a_2,a_3..) in my representation, it means i have used the ruler a_1 + a_2 + a_3 times... woops... i guess it is not trivial at all. ^^ well why don't we just add more numbers in my set if necessary. anyway, at least i give you some direction how to prove the problem. whether it is a winding road, only our Lord will know the answer. ^^ |