Each of C, D, E, F, X, Y and Z has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only two people have exams before D. Only one person has exam after C. Only three people have exams between D and Z. Only one person has exam between X and Y. F has exam immediately before X. How many people have exam(s) between E and X?
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:
| Day | 1 (Mon) | 2 (Tue) | 3 (Wed) | 4 (Thu) | 5 (Fri) | 6 (Sat) | 7 (Sun) |
| Person | _ | _ | D | _ | _ | C | Z |
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.
Important Questions from Puzzle
Seven friends O, P, Q, R, S, T and U are watching a movie sitting in a row. S is sitting at one extreme end. P is sitting second to the right of S. P is sitting between O and Q. U is NOT sitting at any extreme end. R Is sitting to the immediate left of T. Q does not sit beside S.Who is sitting at the extreme left end?
What should come in place of the question mark (?) in the given series?
86, 88, 90, 92, 94, ?G, H, J, K, L and P live on six different floors of the same building. The lowest floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6. Only two people live between P and K. Only two people live between P and H. No one lives above P. K lives below H, but above L. How many people live below G?
Seven students, Q, R, S, T, W, X and Y, are sitting in a straight line facing north. Only two people sit to the right of W. Only two people sit between W and X. Only two people sit between Y and R. R sits to the immediate left of W. S sits to the immediate right of Q. How many people sit between S and T?
R, A, D, I, U and S live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6. Only two people live between I and U. Only A lives above R. D lives on an even numbered floor. I lives on the lowermost floor. How many people live between S and A?
