HMMT 十一月 2010 · GEN2 赛 · 第 4 题

HMMT November 2010 — GEN2 Round — Problem 4

[ 5 ] A zerg player can produce one zergling every minute and a protoss player can produce one zealot every 2.1 minutes. Both players begin building their respective units immediately from the beginning of the game. In a fight, a zergling army overpowers a zealot army if the ratio of zerglings to zealots is more than 3. What is the total amount of time (in minutes) during the game such that at that time the zergling army would overpower the zealot army?

解析

[ 5 ] A zerg player can produce one zergling every minute and a protoss player can produce one zealot every 2.1 minutes. Both players begin building their respective units immediately from the beginning of the game. In a fight, a zergling army overpowers a zealot army if the ratio of zerglings to zealots is more than 3. What is the total amount of time (in minutes) during the game such that at that time the zergling army would overpower the zealot army? Answer: 1.3 At the end of the first minute, the zerg player produces a zergling and has a superior army for the 1 . 1 minutes before the protoss player produces the first zealot. At this point, the zealot is at least a match for the zerglings until the fourth is produced 4 minutes into the game. Then, the zerg army has the advantage for the . 2 minutes before a second zealot is produced. A third zealot will be produced 6 . 3 minutes into the game, which will be before the zerg player accumulates the 7 zerglings needed to overwhelm the first 2 zealots. After this, the zerglings will never regain the advantage because the zerg player can never produce 3 more zerglings to counter the last zealot before another one is produced. So, the zerg player will have the military advantage for 1 . 1 + . 2 = 1 . 3 minutes. Theme Round