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![]() | Text and/or other creative content from Hat puzzle was copied or moved into Induction puzzles. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
![]() | Text and/or other creative content from Muddy children puzzle was copied or moved into Induction puzzles. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
In general, if there are n unfaithful husbands, each of their wives will believe there to be n-1 and will expect to hear a gunshot at midnight on the n-1th day. When they don't, they know their own husband was the nth.
Isn't the above statement incorrect? Gunshot will always be heard on the second day for any case other than n<2. For n =>2 the wives will always be aware of n-1 unfaithful husbands on the first day, hence any wife with an unfaithful husband will always know their husband is the nth unfaithful one on the second day.— Preceding unsigned comment added by Dmsdemon (talk • contribs) 07:45, 24 March 2006
I changed the wording in the solution to the third problem because it made heavy use of the word 'repeated' to mean 'seen' or 'appeared.' For instance, seeing a color "repeated once" means it is seen twice because one must have already seen the color in order for it to be repeated. --Ddawn23 12:42, 19 November 2006 (UTC)
The solution to the third problem also has many wording/grammar issues starting with the italicized portion. Someone with more knowledge of the logic problem should probably rewrite that part. --Larryhl45 (talk) 07:28, 19 July 2015 (UTC)
I added a note to the first solution to explain the flaw in its statement. For people who aren't too worried about it, I left the statement and the answer completely unchanged, and only added a final note after the other comments in the answer.Frentz 08:07, 22 October 2007 (UTC)
There is a flaw in the answer. The first man could be wearing a white or blue hat, there is no certainty that they are all wearing blue hats — Preceding unsigned comment added by 145.100.112.108 (talk) 08:15, 7 February 2019 (UTC)
I propose to merge Muddy children puzzle into Induction puzzles. The puzzle does not seem to be fundamentally different from other induction puzzles, and would be best served by being presented in the context of the similar puzzles in this article. Sneftel (talk) 08:23, 19 February 2020 (UTC)
The description of the Muddy children puzzle and the solution can be greatly clarified:
A group of children is told that some of them have muddy faces. Each child can see the faces of the others, but cannot tell if his or her own face is muddy. The children are told that those with muddy faces must step forward, but any child with a clean face who steps forward will be punished. At the count of three, every child who believes that his or her face is muddy must step forward simultaneously; any child who signals to another in any way will be punished. If any child with a muddy face has not stepped forward, the process will be repeated.
If, and only if, each child has and knows each of the others to have perfect logic, all children with muddy faces (X) will step forward together on turn X. The children have different information, depending on whether their own faces are muddy or not. Each member of X sees X-1 muddy faces, and knows that those children will step forward on turn X-1 if they are the only muddy faces. When that does not occur, each member of X knows that he or she is also a member of X, and steps forward on turn X. Each non-member of X sees X muddy faces, and will not expect anyone to step forward until turn X:
Rickwodz (talk) 17:19, 18 December 2020 (UTC)