Question

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 own cottage. There are no others staying in the same row of houses.
1. Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row.
2. Eliza and Anne are unwilling to stay besides any occupied cottage.
3. Karen is next to Peter and Jack.
4. Between Anne and Jack’s cottage there is just one vacant house.
5. None of the girls occupy adjacent cottages.
6. The house occupied by Tom is next to an end cottage.

Q. How many of them occupy cottages next to a vacant cottage?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is C

4

Rule 6:
_ T _ _ _ _ _ _ _
_ _ _ _ _ _ _ T _

Rule 3:
_ T P K J _ _ _ _
_ T _ P K J _ _ _
_ T _ _ P K J _ _
_ T _ _ _ _ P K J
P K J _ _ _ _ T _
_ P K J _ _ _ T _
_ _ P K J _ _ T _
_ _ _ P K J _ T _
_ _ _ _ P K J T _

Rule 2 says that there has to be 2 spaces where there are no neighbors. That eliminates:
_ T P K J _ _ _ _
_ T _ P K J _ _ _ <-- This one
_ T _ _ P K J _ _ <-- This one
_ T _ _ _ _ P K J <-- This one
P K J _ _ _ _ T _ <-- This one
_ P K J _ _ _ T _ <-- This one
_ _ P K J _ _ T _ <-- This one
_ _ _ P K J _ T _ <-- This one
_ _ _ _ P K J T _

Leaving us with:
_ T P K J _ _ _ _
_ _ _ _ P K J T _

Rule 4 says there must be 1 slot between Jack and Anne. If I flip the order P K J are in:
_ T P K J _ _ _ _
_ _ _ _ J K P T _

Then:
_ T P K J _ A _ _
_ _ A _ J K P T _

From Rule 2:
_ T P K J _ A _ E
E _ A _ J K P T _

Rule 5 is a restatement of rule 2. If 2 of the 3 girls don't have any neighbors, then the 3rd girl can't be next to a girl, because those girls don't have neighbors. Both of these solutions meet your criteria.
_ T P K J _ A _ E
E _ A _ J K P T _