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 problem, we can use a systematic approach and make deductions based on the given statements:

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 there are only 6 available cottages for them.

Statement B states that Eliza and Anne are unwilling to stay beside any occupied cottage. Let's consider the possibilities based on this statement.

We know that Karen is next to Peter and Jack (Statement C). So, we have:
_Karen__Peter__Jack_ (empty cottages)

Now, let's consider Statement D, which says that between Anne and Jack's cottage there is just one vacant house.

We have two possible scenarios:

1. If Anne is on the left side:
_Karen__Peter__Jack__Anne_ (empty cottages)

2. If Anne is on the right side:
_Karen__Peter__Anne__Jack_ (empty cottages)

Now let's consider Statement E, which states that none of the girls can occupy adjacent cottages. Based on this, we can determine the possible positions for Eliza and Anne.

For the first scenario (Anne on the left side):
_Karen__Peter__Jack__Anne__Eliza_ (empty cottages)

For the second scenario (Anne on the right side):
_Karen__Peter__Anne__Jack__Eliza_ (empty cottages)

Finally, let's consider Statement F, which tells us that the house occupied by Tom is next to an end cottage. We have two possibilities for Tom's position:

1. If Tom is on the left end:
_Karen__Peter__Jack__Anne__Eliza__Tom_ (empty cottages)

2. If Tom is on the right end:
_Karen__Peter__Anne__Jack__Eliza__Tom_ (empty cottages)

We have exhausted all the given statements, and we have found all the possible arrangements. By analyzing these arrangements, we can answer the questions:

- How many of them occupy cottages next to a vacant cottage?
In both arrangements, only Karen and Peter occupy cottages next to a vacant cottage. So, 2 people occupy cottages next to a vacant cottage.

- Which among these statements are true?
1. Annie is between Eliza and Jack - This statement is not true in any of the arrangements.
2. At most four persons can have occupied cottages on either side of them - This statement is not true. In both arrangements, it's only possible to have three persons with occupied cottages on either side of them.
3. Tom stays beside Peter - This statement is true in both arrangements.

So, the correct answer is: 2 people occupy cottages next to a vacant cottage, and statement 3 is true (Tom stays beside Peter).