HMMT 十一月 2010 · GEN2 赛 · 第 4 题

英文解析

4. [ 5 ] A zerg player can produce one zergling every minute and a protoss player can produce one zealotevery 2.1 minutes. Both players begin building their respective units immediately from the beginningof the game. In a fight, a zergling army overpowers a zealot army if the ratio of zerglings to zealots ismore than 3. What is the total amount of time (in minutes) during the game such that at that timethe 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 superiorarmy for the 1 . 1 minutes before the protoss player produces the first zealot. At this point, the zealot isat least a match for the zerglings until the fourth is produced 4 minutes into the game. Then, the zergarmy has the advantage for the . 2 minutes before a second zealot is produced. A third zealot will beproduced 6 . 3 minutes into the game, which will be before the zerg player accumulates the 7 zerglingsneeded to overwhelm the first 2 zealots. After this, the zerglings will never regain the advantagebecause the zerg player can never produce 3 more zerglings to counter the last zealot before anotherone is produced. So, the zerg player will have the military advantage for 1 . 1 + . 2 = 1 . 3 minutes.
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