Determining Exam Schedule

The problem requires determining the order of exams for 7 people (C, D, E, F, X, Y, Z) across 7 days (Monday to Sunday). We use the given clues to establish the schedule.

Constraint Application

• Clue: "Only two people have exams before D." This implies D's exam is on the 3rd day. Let Monday be Day 1. So, D is on Wednesday (Day 3).
• Clue: "Only one person has exam after C." This implies C's exam is on the 6th day, Saturday (Day 6).
• Clue: "Only three people have exams between D and Z." With D on Day 3, Z must be on Day 7 (Sunday) to allow for exactly three people (on Days 4, 5, and 6) between them.

Based on these clues, the partial schedule is:

Resolving Remaining Positions

• Remaining people: E, F, X, Y.
• Remaining days: 1 (Mon), 2 (Tue), 4 (Thu), 5 (Fri).
• Clue: "F has exam immediately before X." This forms an "FX" block.
• Clue: "Only one person has exam between X and Y."

We evaluate the possible positions for the "FX" block:

• Option 1: FX block on Days 1, 2.
  • Schedule: F(1), X(2), D(3), _, _, C(6), Z(7).
  • Remaining people E, Y for Days 4, 5.
  • Constraint "One person between X and Y": With X on Day 2, Y must be on Day 4 to have D (Day 3) between them. This fits the constraint. So, Y is Day 4.
  • This leaves E for Day 5.
  • The valid schedule is: F(1), X(2), D(3), Y(4), E(5), C(6), Z(7).
• Option 2: FX block on Days 4, 5.
  • Schedule: _, _, D(3), F(4), X(5), C(6), Z(7).
  • Remaining people E, Y for Days 1, 2.
  • Constraint "One person between X and Y": With X on Day 5, Y cannot be placed to satisfy this. If Y is Day 2, then D(3) and F(4) are between X(5) and Y(2), violating the "only one person" rule. If Y is Day 1, there are D(3), F(4), X(5) between them, also invalid. This option is not possible.

Therefore, the only valid schedule is F(Mon), X(Tue), D(Wed), Y(Thu), E(Fri), C(Sat), Z(Sun).

Calculating Exams Between E and X

From the derived schedule:

• E's exam is on Friday (Day 5).
• X's exam is on Tuesday (Day 2).
• The days scheduled between Day 2 and Day 5 are Day 3 (Wednesday) and Day 4 (Thursday).
• The people scheduled on these days are D and Y.
• Thus, there are 2 people with exams between E and X.