Solving the Six Person Scheduling Logic Puzzle

This question is a classic logic puzzle where we need to determine the working day for each of the six persons (A, B, C, D, E, F) based on the given clues. The six days are Sunday through Friday.

Understanding the Schedule and Clues

The six days available for work are Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday. There is exactly one person working on each of these days. Let's list the days:

• Sunday
• Monday
• Tuesday
• Wednesday
• Thursday
• Friday

The persons are A, B, C, D, E, and F.

We are given the following clues:

• Clue 1: Three persons work between A and F.
• Clue 2: Two persons work between B and D.
• Clue 3: E works on Monday.
• Clue 4: C works after D, but before F.

Step-by-Step Deduction of the Schedule

Let's start by placing the person with a fixed day based on the clues.

From Clue 3, we know that E works on Monday. Let's place E in our tentative schedule:

Now let's use Clue 1: Three persons work between A and F. This means there are exactly three days between A's working day and F's working day. Given there are 6 days (Sunday to Friday), the possible pairs of days for A and F with three days in between are:

• Sunday and Thursday (Days in between: Monday, Tuesday, Wednesday - 3 days)
• Monday and Friday (Days in between: Tuesday, Wednesday, Thursday - 3 days)

However, from Clue 3, E works on Monday. So, neither A nor F can work on Monday. This eliminates the second possibility (Monday and Friday) for the pair A and F.

Therefore, A and F must work on Sunday and Thursday. There are two possibilities:

1. A works on Sunday and F works on Thursday.
2. F works on Sunday and A works on Thursday.

Let's consider Clue 4: C works after D, but before F. This implies the chronological order of working days is D, then C, then F. D's day < C's day < F's day.

Let's evaluate the two possibilities for A and F:

Evaluating Possibility 1: A on Sunday, F on Thursday

Remaining days: Tuesday, Wednesday, Friday. Remaining persons: B, C, D.

From Clue 4 (D -> C -> F), D and C must work before F (Thursday). The available days before Thursday are Tuesday and Wednesday. Thus, D and C must work on Tuesday and Wednesday, with D on Tuesday and C on Wednesday (since D works before C).

This gives us the partial schedule:

The only remaining day is Friday, and the only remaining person is B. So, B must work on Friday.

Proposed schedule:

Let's verify this schedule with all the clues:

• Clue 1 (3 between A and F): A is on Sunday, F is on Thursday. The persons working on days between Sunday and Thursday are E (Mon), D (Tue), C (Wed). There are exactly 3 persons between A and F. This fits.
• Clue 2 (2 between B and D): B is on Friday, D is on Tuesday. The persons working on days between Tuesday and Friday are C (Wed), F (Thu). There are exactly 2 persons between B and D. This fits.
• Clue 3 (E on Monday): Yes, E is on Monday. This fits.
• Clue 4 (C after D, before F): D is on Tuesday, C is on Wednesday, F is on Thursday. Tuesday < Wednesday < Thursday. D works before C, and C works before F. This fits.

All clues fit this schedule. This is the correct schedule.

Evaluating Possibility 2: F on Sunday, A on Thursday

If F works on Sunday, then according to Clue 4 (C works before F), C must work before Sunday. This is not possible as Sunday is the first day of the week in this schedule. So, this possibility is invalid.

Thus, the only possible schedule is:

Analyzing the Statements

Now we need to check the given statements based on the final schedule.

Statement I: B works on Friday.

Looking at the schedule, B works on Friday. This statement is Correct.

Statement II: C works on Wednesday.

Looking at the schedule, C works on Wednesday. This statement is Correct.

Both statements I and II are correct.

Conclusion

Based on the deduction from the given clues, the final schedule is A on Sunday, E on Monday, D on Tuesday, C on Wednesday, F on Thursday, and B on Friday. Both statement I (B works on Friday) and statement II (C works on Wednesday) are true according to this schedule.

Revision Table: Key Information

Additional Information on Logic Puzzles and Scheduling

Logic puzzles involving scheduling or ordering require careful step-by-step deduction. It's often helpful to:

• Identify any fixed positions first (like E on Monday in this case).
• Use clues about the number of items/people "between" others to narrow down possibilities for their positions.
• Use clues about relative order (like 'after' or 'before') to establish sequences.
• Combine different clues to eliminate possibilities. For example, combining the A/F clue with the E on Monday clue significantly reduced the options for A and F.
• Represent the information visually, like using a table or drawing slots for days, can help organize thoughts.
• Always verify the final solution against ALL the original clues to ensure consistency.

These types of puzzles are common in aptitude tests and help develop analytical and logical reasoning skills.