| [ QuizWit ] in KIDS 글 쓴 이(By): ilusion (luVthYsouL맧) 날 짜 (Date): 1997년11월01일(토) 18시06분56초 ROK 제 목(Title): ANSWER TO STONE PICKING Need to solve simultaneous recurrence equations. Solve teh following b_n = b_(n-1) + [ b_(n-1)/2 ] where [] is the ceiling function with the initial condition b_1 = 2 Where b_n stands for the second player wining. you will have 2,3,5,5+3,8+4,12+6,18+9,27+14 ...... The first player will win with 6,7 stones than it is obvious the second player will win with 8 stones (why? 8 = 1+7,2+6 and 3+5 decompostion is forbidden!) Now you figure out how to solve the above recurrence. It is also easy. Just figure out even or odd terms. or multiply both side by 2. iLUSiON chung@math.mcgill.ca chung@math.toronto.edu |