2023 AMC 8 第 8 题

先试着解答 2023 AMC 8 第 8 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2023 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

8.

洛拉、洛洛、蒂娅和蒂约参加乒乓球比赛。每位选手都与另外三位选手各比赛两次。下方显示了选手们的胜负记录。数字 11 和 00 分别表示胜和负。例如,洛拉赢了五场,输了第四场。蒂约的胜负记录是什么?
Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three players exactly twice. Shown below are the win-loss records for the players. The numbers 11 and 00 represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo’s win-loss record?
000101000101
001001001001
010000010000
010101010101
011000011000
答案:A
知识点:逻辑推理奇偶性
小提示:
每场比赛贡献一个胜和一个负
Each match contributes one win and one loss
大提示:
每列记录中必须有两个数等于 11,另两个数等于 00
In each column of the records, two entries must equal 11 and two must equal 00
视频讲解:
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文字解答:
每一列代表同一轮的两场比赛,因此恰好包含两个胜场记录 11 和两个负场记录 00。
逐列填入使该列达到两个 11 和两个 00 所需的数,得到蒂约的胜负记录为 000101000101。
所以正确答案是 A。
Each column represents one round of two matches, so every column must contain exactly two 11’s and two 00’s.
Completing each column to contain two 11 entries and two 00 entries gives Tiyo’s record 000101.000101.
Thus, A is the correct answer.
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