HMMT 二月 2000 · GEN 赛 · 第 8 题
HMMT February 2000 — GEN Round — Problem 8
题目详情
英文原题
- Bob o the lo wn w as juggling his spheri al o ws again when he realized that when hedrops a o w is related to ho w man y o ws he started o juggling. If he juggles 1, hedrops it after 64 se onds. When juggling 2, he drops one after 55 se onds, and the other
55 se onds later. In fa t, he w as able to reate the follo wing table:
o ws started juggling 1 2 3 4 5 6 7 8 9 10 11
se onds he drops after 64 55 47 40 33 27 22 18 14 13 12
o ws started juggling 12 13 14 15 16 17 18 19 20 21 22
se onds he drops after 11 10 9 8 7 6 5 4 3 2 1
He an only juggle up to 22 o ws. T o juggle the o ws the longest, what number of o wsshould he start o juggling? Ho w long (in min utes) an he juggle for?
解析
英文解析
- The time that Bob o an juggle is the number of o ws times se onds. So, we get thefollo wing table:
o ws started juggling 1 2 3 4 5 6 7 8 9 10 11
total time 64 110 141 160 165 162 154 144 126 130 132
o ws started juggling 12 13 14 15 16 17 18 19 20 21 22
total time 132 130 126 120 112 102 90 76 60 42 22
Th us, we see that the maxim um o urs with 5 o ws , and the total time is 165 se onds = 2 min utes .3
x 4