This problem is a classic logical reasoning puzzle involving employee scheduling and work day assignments. We need to determine who among the five employees (A, B, C, D, E) works on Monday, given specific constraints about their working days from Monday to Friday.

Employee Scheduling Constraints Explained

Let's break down the rules provided in the passage for this employee scheduling puzzle:

• There are five employees: A, B, C, D, and E.
• They work from Monday to Friday, with each employee working for only one specific day.
• Constraint 1: D and E will not work on Thursday and Friday. This means D and E must work on Monday, Tuesday, or Wednesday.
• Constraint 2: C will work on the day immediately after E is working. This forms a consecutive pair (E, C).
• Constraint 3: D will work on the day immediately before the B’s working day. This forms another consecutive pair (D, B).

Deduction Steps for Working Days

We need to find out who works on Monday by carefully applying these constraints. Since D and E are restricted to Monday, Tuesday, or Wednesday, these three days are crucial for their assignments. The remaining two days (Thursday and Friday) must be filled by A, B, or C.

Constraint Analysis for Employee Scenarios

1. D and E's Restricted Days: D and E can only work on Monday, Tuesday, or Wednesday. This is a very important constraint as it limits their possible working days.

   This implies that the two consecutive pairs (D, B) and (E, C) must be placed in the week such that D and E fall within Monday, Tuesday, or Wednesday.

2. Analyzing the (D, B) Pair: D must work immediately before B.

   • If D works on Monday, then B works on Tuesday. (D = Mon, B = Tue)
   • If D works on Tuesday, then B works on Wednesday. (D = Tue, B = Wed)
   • If D works on Wednesday, then B works on Thursday. (D = Wed, B = Thu) - This is valid because B is not subject to the Thursday/Friday restriction that applies only to D and E.

3. Analyzing the (E, C) Pair: E must work immediately before C.

   • If E works on Monday, then C works on Tuesday. (E = Mon, C = Tue)
   • If E works on Tuesday, then C works on Wednesday. (E = Tue, C = Wed)
   • If E works on Wednesday, then C works on Thursday. (E = Wed, C = Thu) - This is valid because C is not subject to the Thursday/Friday restriction.

Working Days: Combining Constraints for Monday

Let's explore the possible arrangements by combining all the conditions and see who could work on Monday:

Scenario 1: D Works on Monday

• If D works on Monday, then based on Constraint 3 (D before B), B must work on Tuesday.
• Now, D (Monday) and B (Tuesday) are assigned.
• Employee E cannot work on Monday or Tuesday as those days are taken. Given Constraint 1 (E works Mon/Tue/Wed), E must work on Wednesday.
• If E works on Wednesday, then based on Constraint 2 (C after E), C must work on Thursday.
• The days assigned so far are: D-Monday, B-Tuesday, E-Wednesday, C-Thursday.
• The only remaining day is Friday, and the only remaining employee is A. Therefore, A works on Friday.
• Let's verify this complete schedule:
  • Monday: D
  • Tuesday: B
  • Wednesday: E
  • Thursday: C
  • Friday: A
• This schedule satisfies all original constraints:
  • D (Monday) and E (Wednesday) are not on Thursday/Friday. (Satisfied)
  • C (Thursday) works immediately after E (Wednesday). (Satisfied)
  • D (Monday) works immediately before B (Tuesday). (Satisfied)
• In this valid scenario, D works on Monday.

Scenario 2: E Works on Monday

• If E works on Monday, then based on Constraint 2 (C after E), C must work on Tuesday.
• Now, E (Monday) and C (Tuesday) are assigned.
• Employee D cannot work on Monday or Tuesday. Given Constraint 1 (D works Mon/Tue/Wed), D must work on Wednesday.
• If D works on Wednesday, then based on Constraint 3 (D before B), B must work on Thursday.
• The days assigned so far are: E-Monday, C-Tuesday, D-Wednesday, B-Thursday.
• The only remaining day is Friday, and the only remaining employee is A. Therefore, A works on Friday.
• Let's verify this complete schedule:
  • Monday: E
  • Tuesday: C
  • Wednesday: D
  • Thursday: B
  • Friday: A
• This schedule also satisfies all original constraints:
  • D (Wednesday) and E (Monday) are not on Thursday/Friday. (Satisfied)
  • C (Tuesday) works immediately after E (Monday). (Satisfied)
  • D (Wednesday) works immediately before B (Thursday). (Satisfied)
• In this valid scenario, E works on Monday.

Conflicting Scenarios Eliminated

Let's briefly consider other initial placement possibilities for the pairs (D,B) or (E,C) to confirm they lead to conflicts:

• If the pair (D, B) is placed as (Tuesday, Wednesday): D=Tue, B=Wed. Remaining days for E, C, A are Monday, Thursday, Friday. E must take Monday (due to Constraint 1). If E=Mon, then C=Tue. But Tuesday is already assigned to D. This creates a conflict, so this placement is not possible.
• If the pair (E, C) is placed as (Tuesday, Wednesday): E=Tue, C=Wed. Remaining days for D, B, A are Monday, Thursday, Friday. D must take Monday (due to Constraint 1). If D=Mon, then B=Tue. But Tuesday is already assigned to E. This creates a conflict, so this placement is not possible.

Therefore, only the two scenarios detailed above are consistent with all the given conditions.

Monday's Worker: Final Conclusion

Based on our detailed logical deduction, we have found two distinct but valid schedules that satisfy all the given employee scheduling constraints:

Both Scenario 1 and Scenario 2 are completely consistent with the problem's rules. This means that the employee working on Monday could be either D or E.