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. Which among these statement(s) are true ? 1. Anne 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

  1. 1 OLY

  2. 2 OLY

  3. 1 AND 3 OLY

  4. 1, 2 AND 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By systematically applying all six constraints (no ends for Anne/Tom/Jack, Eliza/Anne beside occupied cottages, Karen next to Peter and Jack, one vacant between Anne and Jack, girls not adjacent, Tom beside end cottage), we can determine the valid cottage arrangements. Statement 1 (Anne between Eliza and Jack) and Statement 3 (Tom beside Peter) are true, while Statement 2 about four persons having occupied cottages on either side is incorrect.

AI explanation

To solve this question, let's go through each statement and determine if it is true or false.

Statement 1: Anne is between Eliza and Jack. This statement is true. From the given information, we know that Karen is next to Peter and Jack. Since Anne, Tom, and Jack do not want to stay in any cottage at the end of the row, it means that Eliza must be at one end of the row, and Jack must be at the other end. Therefore, Anne must be between Eliza and Jack.

Statement 2: At most four persons can have occupied cottages on either side of them. This statement is false. If Tom stays next to an end cottage and Anne, Tom, and Jack do not want to stay in any cottage at the end of the row, it means that Tom cannot have more than one person on his side. Therefore, at most three persons can have occupied cottages on either side of Tom.

Statement 3: Tom stays besides Peter. This statement is true. From the given information, we know that Karen is next to Peter and Jack. Since Tom stays next to an end cottage, it means that Tom can only be next to Peter.

Based on our analysis, the correct statements are 1 and 3. Therefore, the correct answer is option C: 1 and 3 only.

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