It should be noted that Anne, Eliza, Karen, Tom, Peter, Jack, a vacant cottage and the occupied cottage are represented respectively by A, E, K, T, P, J, , and . As Karen is next to Peter and Jack (as cited in statement 3), the arrangement of the cottages should be either

1. 

   As Anne refused to live in an end cottage (as cited in statement 1), and Eliza and Anne do not want to live next to an occupied cottage (as cited in statement 2), the partial cottage arrangement is

2. 

   Since there is a vacant house between Anne and Jack (statement 4) and from (1) and (2), we can derive the following arrangement

   or   

   As cited in statement 6 Tom is next to an end house. Hence we can arrive at the arrangement:

3. 

   As cited in Statement 2 Eliza and Anne do not want live next to any occupied cottage. Eliza could not be next to Tom and from (3) and (4) above, the arrangement of the cottages should be:

4.