Question

If the mouse is in chamber 2, and the other four animals are all in chambers, which of the following is a pair of chambers that must be empty?

• A. 1 and 3
• B. 1 and 4
• C. 2 and 4
• D. 3 and 5
• E. 3 and 6
• A. 1
• B. 2
• C. 3
• D. 4
• J. 5
• A. One
• B. Two
• C. Three
• D. Four
• O. Five
• A. 1
• B. 3
• C. 4
• D. 5
• T. 6
• A. The frog and the mouse
• B. The frog and the parakeet
• C. The frog and the rabbit
• D. The mouse and the rabbit
• Y. The parakeet and the rabbit

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a logic game question. We need to apply the given rules to a specific scenario to determine a necessary outcome.
Step 2: Detailed Explanation:
First, let's understand the chamber layout and the rules. - Layout: Two separate rows of 3 chambers. Front: 1-2-3. Back: 4-5-6. Adjacency only exists within a row (1 is adjacent to 2, 2 to 1 and 3, etc.). - Rule 1: Max 2 animals per chamber. (Holds at least 2, but can't contain more than 2). - Rule 2 (Mouse Rule): The mouse (M) must be alone in its chamber, AND its adjacent chambers must be empty. - Rule 3 (Parakeet Rule): The parakeet (P) cannot be with the hen (H) or the frog (F). Now, apply the scenario: 1. The mouse is in chamber 2. 2. According to the Mouse Rule, any chamber "directly adjacent" to chamber 2 must be empty. 3. The chambers directly adjacent to chamber 2 are chamber 1 and chamber 3. 4. Therefore, chambers 1 and 3 must be empty. The other four animals (frog, hen, parakeet, rabbit) must be in the remaining chambers (4, 5, 6). The question only asks which chambers must be empty. Step 3: Final Answer:
The Mouse Rule dictates that chambers 1 and 3, being adjacent to chamber 2, must be empty.

Answer 2

Step 1: Understanding the Concept:
This is a logic game question where we are given a partial arrangement and asked to find a possible location for one of the animals.
Step 2: Detailed Explanation:
1. Analyze the given setup: - Mouse (M) is in chamber 2. - Parakeet (P) is in chamber 4. - The other animals (Frog F, Hen H, Rabbit R) are in other chambers. 2. Apply the Mouse Rule: - M is in chamber 2. M must be alone. - Adjacent chambers 1 and 3 must be empty. 3. Apply the Parakeet Rule: - P is in chamber 4. - Neither the hen (H) nor the frog (F) can be in the same chamber as P. So, H and F are not in chamber 4. 4. Determine available chambers: - Chambers 1 and 3 are empty. - Chamber 2 contains the mouse. - Chamber 4 contains the parakeet. - The only chambers left for the remaining three animals (F, H, R) are 5 and 6. 5. Place the remaining animals: - We have 3 animals (F, H, R) to place in 2 chambers (5 and 6). - Since no chamber can hold more than two animals, one chamber must hold two animals, and one chamber must hold one animal. - The parakeet rule says H cannot be with P (which is in chamber 4). This is already satisfied. - The mouse rule says M must be alone. This is satisfied. - We need to place F, H, and R into chambers 5 and 6. - The hen (H) can be in chamber 5 or chamber 6. Both are valid options. - Let's check the answer choices. Chamber 5 is listed as an option. Chamber 6 is not. - For example, a valid arrangement would be: M in 2; P in 4; H and R in 5; F in 6. This satisfies all rules. In this case, the hen is in chamber 5. Step 3: Final Answer:
Given the constraints, the hen must be in either chamber 5 or 6. Since 5 is an option, it is a possible chamber for the hen.

Answer 3

Step 1: Understanding the Concept:
We are asked to determine the number of possible chambers the mouse can occupy under a new condition: each of the five animals is in a separate chamber, meaning one chamber remains empty. The key constraint is that any chamber directly adjacent to the mouse's chamber must remain empty. Step 2: Detailed Explanation:
1. Setup: - There are 6 chambers arranged in two rows: front row (1-2-3) and back row (4-5-6).
- No front chamber is adjacent to any back chamber.
- Five animals occupy five separate chambers, leaving exactly one chamber empty.
2. Mouse Rule:
- The mouse occupies a chamber, and all chambers directly adjacent to it must be empty.
- In other words, if the mouse is in chamber 1, chamber 2 must be empty; if in 2, both 1 and 3 must be empty, etc.
3. Analyze Each Possible Chamber:
- Mouse in chamber 1:
- Adjacent chamber 2 must be empty.
- Remaining chambers (3, 4, 5, 6) can accommodate the other 4 animals. ✅
- Mouse in chamber 2:
- Adjacent chambers 1 and 3 must be empty.
- Only chambers 4, 5, 6 remain for the other 4 animals, which is insufficient. ❌
- Mouse in chamber 3:
- Adjacent chamber 2 must be empty.
- Remaining chambers (1, 4, 5, 6) can accommodate the other 4 animals. ✅
- Mouse in chamber 4:
- Adjacent chamber 5 must be empty.
- Remaining chambers (1, 2, 3, 6) can accommodate the other 4 animals. ✅
- Mouse in chamber 5:
- Adjacent chambers 4 and 6 must be empty.
- Only chambers 1, 2, 3 remain for the other 4 animals, which is insufficient. ❌
- Mouse in chamber 6:
- Adjacent chamber 5 must be empty.
- Remaining chambers (1, 2, 3, 4) can accommodate the other 4 animals. ✅
4. Count the Possible Chambers:
- The mouse can occupy chambers 1, 3, 4, or 6.
- Chambers 2 and 5 are not possible because having two adjacent chambers empty would leave only 3 chambers for 4 other animals, which is insufficient.
Step 3: Final Answer:
By carefully applying the adjacency rule and the condition that each of the five animals occupies a separate chamber, we find that the mouse can occupy 4 chambers: 1, 3, 4, or 6.

Answer 4

Step 1: Understanding the Concept:
We are asked to determine the exact chamber where the parakeet must be placed, given that the mouse occupies chamber 2 and several placement rules apply. This is a logic deduction problem involving adjacency constraints and multiple animals in limited chambers.
Step 2: Detailed Explanation:
1. Mouse Placement Rule: - The mouse (M) is in chamber 2. - Any chamber directly adjacent to the mouse's chamber must remain empty.
- Chambers 1 and 3 are therefore empty.
- So far: C1 = Empty, C2 = Mouse, C3 = Empty.
2. Determine Available Chambers for Remaining Animals: - The remaining animals are Frog (F), Hen (H), Parakeet (P), and Rabbit (R).
- The remaining chambers are 4, 5, and 6 in the back row.
- These 4 animals need to occupy 3 chambers. At least one chamber must hold two animals.
3. Apply Frog/Hen Rule: - "The frog's chamber is different from and not directly adjacent to the hen's chamber."
- In the back row, the adjacencies are 4-5 and 5-6. The only pair of non-adjacent chambers is 4 and 6.
- Therefore, F and H must occupy the end chambers of the back row: chambers 4 and 6.
- So we assign: F in 4 and H in 6 (order interchangeable).
4. Determine Parakeet Placement: - The remaining animals are Parakeet (P) and Rabbit (R). - The only available chamber is 5. - Therefore, both P and R must be placed in chamber 5. 5. Apply Parakeet Rule: - "Neither the hen nor the frog can be in the same chamber as the parakeet." - P is in chamber 5, F and H are in 4 and 6. The rule is satisfied. 6. Summary of Animal Placement: - C1: Empty - C2: Mouse - C3: Empty - C4: Frog - C5: Parakeet and Rabbit - C6: Hen Step 3: Verification: - All rules are satisfied:
- Mouse adjacency rule: OK (adjacent chambers 1 and 3 empty)
- Frog/Hen non-adjacency: OK (F in 4, H in 6)
- Parakeet not with Frog/Hen: OK (P in 5)
- No other arrangement satisfies all rules simultaneously, so the placement is unique.
Step 4: Final Answer:
The parakeet must be in chamber 5. \textit{Note: This contradicts the provided answer key, which states chamber 4. Based on the rules as given, chamber 5 is the only valid placement.}

Answer 5

Step 1: Understanding the Concept:
This is a logic game question where we need to identify the pair of animals in chamber 3, given the number of animals in each chamber and the placement rules. Step 2: Detailed Explanation:
1. Analyze the given setup:
- C1 contains 2 animals: Hen (H) + 1 other.
- C3 contains 2 animals.
- C5 contains 1 animal.
- Chambers 2, 4, and 6 are empty. 2. Apply the Mouse Rule:
- The mouse (M) must be alone, and adjacent chambers must be empty.
- C1 and C3 both have 2 animals, so M cannot be in either.
- Only C5 is singly occupied with empty neighbors (C4 and C6), so M must be in C5. 3. Apply the Parakeet Rule:
- The Parakeet (P) cannot share a chamber with the Hen (H) or Frog (F).
- H is in C1, so P cannot go there. 4. Determine the remaining placements:
- Animals left to place: Frog (F), Parakeet (P), Rabbit (R).
- C1 needs 1 more animal. P cannot be with H, so F must go there.
- C3 needs 2 animals. The remaining animals are P and R, so they must go in C3. 5. Final Arrangement:
- C1: Hen + Frog (H, F)
- C3: Parakeet + Rabbit (P, R)
- C5: Mouse (M)
- C2, C4, C6: Empty 6. Answer the Question:
- Chamber 3 must contain Parakeet and Rabbit. \textit{Note: The provided answer key (C) suggests Frog and Rabbit, but this is logically impossible under the rules. The correct answer is (E).}