Meeting Schedule Analysis

This problem requires us to determine the exact order in which seven people (A, B, C, D, E, F, and G) attend a meeting on different days of the week, based on a series of clues. We need to find out how many people attend the meeting between B and A.

Identifying Key Constraints

Here are the specific conditions provided:

• People: A, B, C, D, E, F, G
• Days: The week consists of Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. The week starts on Monday.
• Clue 1: B attends on Thursday.
• Clue 2: Exactly one person is scheduled between B and G.
• Clue 3: A attends the meeting on the day immediately following G's meeting.
• Clue 4: The count of people attending meetings before A is the same as the count of people attending meetings after C.
• Clue 5: Exactly one person is scheduled between C and D.
• Clue 6: F attends the meeting on a day after D.

Step-by-Step Schedule Deduction

Let's build the schedule systematically:

Step 1: Placing B

From Clue 1, we know B attends on Thursday.

Step 2: Placing G and A

Clue 2 states there is one person between B (Thursday) and G. This means G could be on Tuesday (with Wednesday between them) or Saturday (with Friday between them). Clue 3 states A attends immediately after G.

• Scenario 1: If G is on Tuesday, A must be on Wednesday.
• Scenario 2: If G is on Saturday, A must be on Sunday.

Step 3: Applying the 'Before A = After C' Rule

Let's test the scenarios using Clue 4 (People before A = People after C):

• Testing Scenario 1 (G=Tue, A=Wed): A is on Wednesday. People before A are Monday and Tuesday (2 people). Thus, there must be 2 people after C. If C attends on Friday, then Saturday and Sunday are after C (2 people). This fits. The partial schedule is: `_ G A B C _ _`.
• Testing Scenario 2 (G=Sat, A=Sun): A is on Sunday. People before A are Monday to Saturday (6 people). Thus, there must be 6 people after C. This means C must attend on Monday (position 1), as Tuesday to Sunday (6 days) follow. The partial schedule is: `C _ _ B _ G A`.

Step 4: Applying the 'Between C and D' Rule

Now we use Clue 5 (Exactly one person between C and D):

• In Scenario 1 (`_ G A B C _ _`): C is on Friday. If D is on Sunday, then Saturday is the day between C and D. This works. Schedule becomes: `_ G A B C _ D`.
• In Scenario 2 (`C _ _ B _ G A`): C is on Monday. If D is on Wednesday, then Tuesday is the day between C and D. This works. Schedule becomes: `C _ D B _ G A`.

Step 5: Applying the 'F after D' Rule

Finally, we use Clue 6 (F attends after D):

• Checking Scenario 1 (`_ G A B C _ D`): D is on Sunday. F must attend after Sunday. This is impossible since Sunday is the last day of the week. Therefore, Scenario 1 is incorrect.
• Checking Scenario 2 (`C _ D B _ G A`): D is on Wednesday. F must attend after Wednesday. The available days are Tuesday and Friday. F can attend on Friday. This works. The schedule becomes `C _ D B F G A`.

The only person left is E, and the only day left is Tuesday. So, E attends on Tuesday.

Final Meeting Schedule

The complete and confirmed schedule is:

Answering the Question

The question asks: "how many people do attend the meeting between B and A?"

• B attends on Thursday.
• A attends on Sunday.
• Based on the final schedule, the person attending on Friday is F, and the person attending on Saturday is G.
• Both F and G attend the meeting between B (Thursday) and A (Sunday).
• Therefore, there are 2 people attending the meeting between B and A.