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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] [★★★★★] 퀴즈쇼와 평균의 함정
솔바람
2021.11.21 00:30
조회 587
어느 퀴즈쇼에 A, B, C 세 팀이 참가했다.
각 팀의 팀원은 5명이고, 퀴즈쇼는 총 3라운드에 걸쳐 진행된다.
각 라운드별로 3문제가 주어지고, 한 문제당 배점은 12점이다.
라운드가 시작될 때마다 팀별로 적어도 한 명씩 참가하며, 마지막 라운드까지 모든 팀원이 참가해야 한다.
단, 한번 참가했던 팀원은 다른 라운드에 다시 참가할 수 없다.
(한 팀의 예시: 1라운드에 a, b 참가 / 2라운드에 c 참가 / 3라운드에 d, e 참가)
퀴즈쇼가 끝난 후, 결과를 분석하였더니 다음과 같았다.
각각의 팀이 기록한 점수의 평균점을 구하여 비교했더니 A, B, C 순으로 높았던 라운드는 1, 2라운드였다.
팀 평균점 점수값이 겹치는 경우는 딱 한 번만 있었다.
(예시: 0, 6, 8, 12, 16, 18, 24, 24, 30)
각 라운드의 팀 평균점을 구하여 합한 값을 비교했더니 A, B, C 순으로 높았다.
(한 팀의 예시: 1라운드에 a, b가 참가하여 24점을 기록했다면 평균점은 12점 / 2라운드에 c가 참가하여 36점을 기록했다면 평균점은 36점
3라운드에 d, e가 참가하여 12점을 기록했다면 평균점은 6점 => 합하면 12 + 36 + 6 = 54점)
3문제를 모두 맞춘 만점자는 A팀과 B팀에만 있었다.
C팀은 한 라운드에 3명을 출전시킨 적이 없다.
그렇다면 C팀이 1등을 하고, A팀이 꼴등을 하는 경우는 결과가 어떨 때일까?
-
솔바람
Lv.10
2021.11.21 00:34
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