推理生日
Birthday Problem
题目详情
老板 A 的生日在以下 10 个日期之一：
Mar 4, Mar 5, Mar 8, Jun 4, Jun 7, Sep 1, Sep 5, Dec 1, Dec 2, Dec 8。
A 只告诉你月份，只告诉同事 C 日期。
你说：“我不知道生日；而且我知道 C 也不知道。”
C 听后说：“我之前不知道，但现在我知道了。”
你再说：“现在我也知道了。”
行政助理听完这些话也写下了正确日期。问：助理写下的是哪一天？
You and your colleague know your boss A’s birthday is one of these 10 dates: Mar 4, Mar 5, Mar 8, Jun 4, Jun 7, Sep 1, Sep 5, Dec 1, Dec 2, Dec 8. A tells you only the month, and tells your colleague only the day. You first say: “I don’t know A’s birthday; C also doesn’t know it.” After hearing this, your colleague C says: “I didn’t know A’s birthday before, but now I know it.” Then you say: “Now I know it too.” The administrative assistant, having heard these statements but asking no questions, writes down the birthday correctly. Which date did the assistant write?
解析
答案是 September 1（9 月 1 日）。
要点：
-
你能确定 C 不知道，说明月份不可能是 Jun 或 Dec（因为它们包含唯一日期 7 或 2/8，C 若拿到这些就会立刻知道）。因此月份只能是 Mar 或 Sep。
-
C 现在能确定日期，说明日期不可能是 5（因为 Mar 5 和 Sep 5 都存在）。于是只剩 Sep 1。
-
你也因此确定为 Sep 1。
Original Explanation
The date is September 1. The reasoning uses the logic from the statements:
- “I don’t know the birthday” means the month must appear more than once in the list. “C also doesn’t know” implies the day is not uniquely identifying a single date (like 7 or 2 would), so the possible months become March or September.
- Once you say that, C then knows the exact date. That means the day cannot be 5 (which occurs in March and September).
- Hence, the date must be Sep 1. Then you also figure it out from the elimination of day=5.