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Six friends went to a Cyber Cafe. They a...

Six friends went to a Cyber Cafe. They are to be accommodated in a row of nine rooms, each to a room. A, E and F do not want to be in a room at the end of the row. B and A must not have anybody adjacent to their rooms, There is only an empty room between A and F. C is adjacent to both G and F. E is next to the room at the beginning.
Who has empty rooms on both sides?

A

F

B

B

C

A

D

E

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to accommodate six friends (A, B, C, E, F, G) in a row of nine rooms while adhering to the given conditions. Let's break down the solution step by step. ### Step 1: Understand the constraints 1. A, E, and F cannot occupy the last room (Room 9). 2. B and A must not have anyone adjacent to their rooms. 3. There must be one empty room between A and F. 4. C is adjacent to both G and F. 5. E is next to the room at the beginning (Room 1). ### Step 2: Set up the rooms We label the rooms from 1 to 9: - Room 1, Room 2, Room 3, Room 4, Room 5, Room 6, Room 7, Room 8, Room 9. ### Step 3: Place E Since E is next to the room at the beginning, E must be in Room 2: - Room 1: Empty - Room 2: E - Room 3: Empty - Room 4: Empty - Room 5: Empty - Room 6: Empty - Room 7: Empty - Room 8: Empty - Room 9: Empty ### Step 4: Place A and F Since A and F cannot be in Room 9, and there must be one empty room between A and F, we can place A in Room 4 and F in Room 6: - Room 1: Empty - Room 2: E - Room 3: Empty - Room 4: A - Room 5: Empty - Room 6: F - Room 7: Empty - Room 8: Empty - Room 9: Empty ### Step 5: Place C and G C must be adjacent to both G and F. Since F is in Room 6, C can be placed in Room 5, and G can be placed in Room 7: - Room 1: Empty - Room 2: E - Room 3: Empty - Room 4: A - Room 5: C - Room 6: F - Room 7: G - Room 8: Empty - Room 9: Empty ### Step 6: Place B B must not have anyone adjacent to their room. The only available room for B that meets this condition is Room 1: - Room 1: B - Room 2: E - Room 3: Empty - Room 4: A - Room 5: C - Room 6: F - Room 7: G - Room 8: Empty - Room 9: Empty ### Final Arrangement Now, we have the following arrangement: - Room 1: B - Room 2: E - Room 3: Empty - Room 4: A - Room 5: C - Room 6: F - Room 7: G - Room 8: Empty - Room 9: Empty ### Step 7: Identify who has empty rooms on both sides From the arrangement: - Room 1 (B) has no one on the left but E on the right. - Room 2 (E) has B on the left and an empty room on the right. - Room 3 is empty. - Room 4 (A) has an empty room on both sides (Room 3 and Room 5). - Room 5 (C) has A on the left and F on the right. - Room 6 (F) has C on the left and G on the right. - Room 7 (G) has F on the left and an empty room on the right. - Room 8 is empty. - Room 9 is empty. Thus, the only person who has empty rooms on both sides is **A**. ### Conclusion **Answer: A has empty rooms on both sides.**

To solve the problem, we need to accommodate six friends (A, B, C, E, F, G) in a row of nine rooms while adhering to the given conditions. Let's break down the solution step by step. ### Step 1: Understand the constraints 1. A, E, and F cannot occupy the last room (Room 9). 2. B and A must not have anyone adjacent to their rooms. 3. There must be one empty room between A and F. 4. C is adjacent to both G and F. 5. E is next to the room at the beginning (Room 1). ...
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