陌生人宣布“城里有出轨者”：第 10 天早上首次被赶出的
stranger will visit the town
题目详情
在一个母系小镇里，女人们相信预言：会有陌生人来访并宣布镇上是否存在男人对妻子不忠。陌生人只会说“是”或“否”，不会透露人数或身份。
规则：陌生人宣布后，如果某位妻子在某天推断出自己丈夫不忠，则她必须在第二天上午 10 点把丈夫赶出家门。所有人都能立刻观察到谁被赶出去。每位妻子都能看出除自己丈夫外的其他男人是否不忠，但不能与他人交流；出轨者也不会承认。
陌生人到来并宣布镇上存在出轨者。第 10 天早上第一次有人被赶出家门。问：有多少个出轨男人？
In a certain matriarchal town, the women all believe in an old prophecy that says there will come a time when a stranger will visit the town and announce whether any of the men folk are cheating on their wives. The stranger will simply say "yes" or "no," without announcing the number of men implicated or their identities. If the stranger arrives and makes his announcement, the women know that they must follow a particular rule: If on any day following the stranger's announcement a women deduces that her husband is not faithful to her, she must kick him out into the street at 10AM the next day. This action is immediately observable by every resident in the town. It is well known that each wife is already observant enough to know whether any man (except her own husband) is cheating on his wife. However, no woman can reveal that information to any other. A cheating husband is also assumed to remain silent about his infidelity.
The time comes, and a stranger arrives. He announces that there are cheating men in the town. On the morning of the tenth day following the stranger's arrival, some unfaithful men are kicked out into the street for the first time. How many of them are
there?
解析
经典归纳结论：如果恰有 个出轨男人，那么在陌生人宣布“至少有 1 个出轨者”后的第 天早上，会有这 个出轨男人第一次同时被赶出。
理由简述：
- 若 ：那位妻子看不到任何出轨者，听到宣布后立刻知道自己丈夫出轨，于是第 1 天早上赶出。
- 归纳：若每位出轨妻子都能看到 个出轨者，那么她会推理：如果自己丈夫忠诚，则应只有 个出轨者，按归纳假设应在第 天早上发生赶出；但她观察到前 天都无人被赶出，于是第 天得知自己丈夫也出轨，并在第 天早上执行。
题目说第 10 天早上首次发生赶出，因此出轨男人数量为 。