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 Knights and Liars of the Round Table (Posted on 2011-06-10)
The Knights and Liars of the Round Table is a group of knights and liars. Each person is either a knight or a liar, and at least one of them is a knight. The number of knights and liars in all is an even number greater than 20, but less than 30. One day, they were sitting around a round table. Each one of them said, "I am sitting between two people of different types." How many people are there in all, and how many are there of each type?

 See The Solution Submitted by Math Man Rating: 3.0000 (1 votes)

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there is at least one knight yet there cant be actually one knight (O) or else he would be lying since 2  liars (X) would have been sitting beside him so there will be 2 knights always sitting beside each other surrounded by 2 liars xOOxOOxOO.... and it seems that we cant break this form since we need the liars always between similar type of people ( which cant be liars since we have at least one knight present)
now looking at the other given clue which is the actual number of the seated party which might be any of ( 22,24,26,28)  we only have one of them that is divisible by 3 which is 24 which is our target since the form which the party are sitting around the round table is (xOO) (XOO) (XOO) and so on... a set of 3 that will close the loop having a lair always between 2 knights and any knights is sitting between another knight and a liar.
in short ... we have 8 liars and 16 knights sitting like this (xOO) (XOO) (XOO) etc. around the table

 Posted by mss on 2011-06-20 17:23:00

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