Three men (Tom, peter, and jack)and three women (Eliza, Anne, and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her owm cottage. There are no others staying in the same row of hoses.In addition,
A. Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row.
B.ELiza and Anne are unwilling to stay besides any occuiped cottage
C. Karen is next to peter and Jack
D. Between Anne and Jack's cottage there is just one vacant house
E. None of the girls occupy adjacent cottages
F. The house occupied by Tom is next to an end cottage.
HOw many of them occupy cottages next to a vacant cottage?
Which among these statements are true?
1. annie is between Eliza and Jack
2. at the most four persons can have occupied cottages on either side of them
3. Tom stays besides peter
To solve this puzzle, let's consider each statement and use deduction to eliminate possibilities until we have a clear solution.
Statement A tells us that Anne, Tom, and Jack do not want to stay in any cottage at the end of the row. This means that their cottages cannot be at positions 1 or 9.
Statement B states that Eliza and Anne are unwilling to stay beside any occupied cottage. We can use this information to eliminate some possibilities. Since Eliza cannot be in the first or last cottage, and Anne cannot be in the second or eighth cottage because they would be next to occupied cottages, we are left with the following possibilities:
_ E _ _ _ _ _ _ _ OR _ _ _ _ _ _ E _ _
Statement C tells us that Karen is next to Peter and Jack. Let's denote Peter as P, Jack as J, and Karen as K. We can use this information along with the possibilities from Statement B. We have two possibilities:
_ E K P J _ _ _ _ OR _ _ _ _ _ P J K E
Statement D states that between Anne and Jack's cottage, there is just one vacant house. Considering the possibilities from Statement C, we can conclude that the following arrangement satisfies this condition:
_ E K P J _ _ _ _
Statement F tells us that the house occupied by Tom is next to an end cottage. The only remaining possibilities that satisfy this condition are:
T E K P J _ _ _ _ OR _ _ _ _ _ P J K T
At this point, we need to consider Statement E, which states that none of the girls can occupy adjacent cottages. The arrangement "_ E K P J _ _ _ _" violates this condition since Eliza and Karen are adjacent. Therefore, we are left with the arrangement:
T E K P J _ _ _ _
Now, let's answer the questions:
1. How many of them occupy cottages next to a vacant cottage?
In this arrangement, there are three people (Eliza, Peter, and Karen) who occupy cottages next to a vacant cottage. They are: E, P, and J.
2. Which among these statements are true?
Among the given options:
1. Annie is between Eliza and Jack - False
2. At most four persons can have occupied cottages on either side of them - False
3. Tom stays beside Peter - True
So, the only true statement is "Tom stays beside Peter."
Therefore, the correct answers are:
1. Three of them occupy cottages next to a vacant cottage.
2. The statement "Tom stays beside Peter" is true.