HMMT 十一月 2010 · GEN2 赛 · 第 1 题

HMMT November 2010 — GEN2 Round — Problem 1

个人笔记

[ 3 ] 16 progamers are playing in a single elimination tournament. Each player has a different skill leveland when two play against each other the one with the higher skill level will always win. Each round,
each progamer plays a match against another and the loser is eliminated. This continues until onlyone remains. How many different progamers can reach the round that has 2 players remaining?

解析

[ 3 ] 16 progamers are playing in a single elimination tournament. Each player has a different skill leveland when two play against each other the one with the higher skill level will always win. Each round,
each progamer plays a match against another and the loser is eliminated. This continues until onlyone remains. How many different progamers can reach the round that has 2 players remaining?
Answer: 9 Each finalist must be better than the person he beat in the semifinals, both of the peoplethey beat in the second round, and all 4 of the people any of those people beat in the first round. So,
none of the 7 worst players can possibly make it to the finals. Any of the 9 best players can make itto the finals if the other 8 of the best 9 play each other in all rounds before the finals. So, exactly 9
people are capable of making it to the finals.