AMC 8 1985 Problem 20
AMC8 1985 年第 20 题
余数与同余★★★☆☆
In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January 1 fall that year?
某年一月份恰好有四个星期二和四个星期六。那年的一月一日是星期几？
- A. / 周一
- B. / 周二
- C. / 周三
- D. / 周五
- E. / 周六
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
January has 31 days, that is, 4 weeks followed by 3 extra days. Since there are only 4 Tuesdays and 4 Saturdays, the 3 extra days must include neither Tuesday nor Saturday. This is only possible if the extra days are Wednesday through Friday. Therefore, January 29 (and thus January 1) is a .
If January 1 was on Monday or Tuesday, then there would be 5 Tuesdays. If January 1 was on Friday or Saturday, there would be 5 Saturdays. This eliminates all choices except .
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