Multiple choice general knowledge math & puzzles

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. Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row. Eliza and Anne are unwilling to stay besides any occupied cottage.. Karen is next to Peter and Jack. Between Anne and Jack’s cottage there is just one vacant house. None of the girls occupy adjacent cottages. The house occupied by Tom is next to an end cottage. How many of them occupy cottages next to a vacant cottage ?

  1. 2

  2. 3

  3. 4

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Based on the cottage arrangement: [Vacant, Tom, Eliza, Vacant, Anne, Vacant, Jack, Karen, Peter], the occupied cottages next to a vacant cottage are Tom, Eliza, Anne, and Jack. This gives a total of 4 people, making 4 the correct answer.

AI explanation

To solve this question, we need to follow the given conditions and determine the number of people who occupy cottages next to a vacant cottage.

Let's analyze each condition:

  1. Anne, Tom, and Jack do not want to stay in any cottage which is at the end of the row.

This means that Anne, Tom, and Jack cannot occupy the first or last cottage in the row.

  1. Eliza and Anne are unwilling to stay beside any occupied cottage.

This means that Eliza and Anne cannot occupy cottages next to any occupied cottage.

  1. Karen is next to Peter and Jack.

This implies that Karen must be occupying a cottage between Peter and Jack.

  1. Between Anne and Jack's cottage, there is just one vacant house.

This means that there is only one empty cottage between Anne and Jack.

  1. None of the girls occupy adjacent cottages.

This condition implies that the girls (Eliza, Anne, and Karen) cannot occupy adjacent cottages.

  1. The house occupied by Tom is next to an end cottage.

This means that Tom must be occupying a cottage next to either the first or last cottage.

Now let's arrange the cottages and determine the occupants:

Considering condition 1, we can eliminate the first and last cottage:

Considering condition 4, we can place Anne and Jack in two consecutive cottages with one vacant cottage between them:

_ _ A J _ _ _ _

Considering condition 5, we know that none of the girls can occupy adjacent cottages, so Eliza cannot be placed in the two vacant cottages next to Anne and Jack. Therefore, Eliza must be placed in one of the outer cottages:

E _ A J _ _ _ _

Considering condition 6, Tom must be placed in one of the two outer cottages:

E _ A J _ _ _ T

Considering condition 2, Eliza cannot be placed in the cottage next to an occupied cottage, so she must be placed in the remaining outer cottage:

E _ A J _ _ K T

Considering condition 3, Karen must be placed between Peter and Jack, so she must be placed in the cottage next to Jack:

E _ A J K _ _

Now we have one vacant cottage left. According to condition 5, none of the girls can occupy this cottage, so Peter must be placed in this cottage:

E _ A J K P _

Therefore, the final arrangement is:

E P A J K P T

From the arrangement, we can see that there are 4 people (Eliza, Anne, Jack, and Karen) who occupy cottages next to a vacant cottage.

Therefore, the correct answer is C) 4.

Keep practicing — related questions