John shows up to his nephew’s sports game without much information. He was given
ID: 3330503 • Letter: J
Question
John shows up to his nephew’s sports game without much information. He was given a list of possible team and field combinations for the game without knowing the name of the team his nephew plays for or the field that the team is playing on. The list John was given is below:
o Golden Eagles on Field 2
o Golden Eagles on Field 3
o Golden Eagles on Field 6
o Gophers on Field 4
o Gophers on Field 5
o Colonials on Field 1
o Colonials on Field 3
o Minutemen on Field 1
o Minutemen on Field 2
o Minutemen on Field 4
John approaches two fans at the complex and inquires for help. He shares the list that he was given. Fan A only knows the team that the nephew plays for. Fan B only knows the field that he is playing on.
Fan A says: I don’t know the team/field combination that you need, but I know that Fan B doesn’t know either.
Fan B replies: I didn’t know the combination, but now after listening to Fan A, I do.
Fan A: Now I know, too!
What is the name of the nephew's team, and what field are they playing on? Explain how you arrived at your answer.
Explanation / Answer
Fan A can only be 100% sure that B does not know the Field if and only if A was told either Colonials or Minutemen. If he was given one of the other two teams, there would have been a chance that B knew the correct filed (i.e. if he was told field 6 or 5, since these two values are unambiguous as easily seen ) and A could not have made his statement. But, since A made his statement, B can deduce (in the same way we just did), that A was told either Colonials or Minutemen.
Both A and B now know that it must be either Colonials or Minutemen. Bernard now tells that he knows and, hence, the Filed 1 can be excluded, since it is found in both Names. If it was Field 1 he could not know.
That leaves three possibilities: ,Colonials Field 3, Minutemen 2 and Minutemen Field 4. Since A states that now he knows, too, it only can be Colonials Field 3, since it is the only unambigous combination of Name and field left.
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