The first player (Annie) doesn't know her number only if she sees two numbers which are in ratio $2:3$ and doesn't know in what case she is. There are $2$ cases where one term of addition is $2/3$ from the other term or is $2/3$ from sum. Is the above conversation plausible or not? Why? The following truthful conversation may or may not take place:Īnnie: I now know my number, and it is 150. Each player is also a perfect logician: anything that they could infer from the information and observations available to them, they instantly will. One of the numbers is equal to exactly two thirds of one of the other numbers.Īnnie, Billy and Katie tell the truth the whole time without exception.One of the numbers is the sum of the other two.The following two things are common knowledge among the players: Each player can only see the foreheads of the other two. Three players, Annie, Billy and Katie, each have a natural number written on their foreheads.
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