Puzzles: Ordering and Scheduling
CSAT · Logical Reasoning
Introduction
Ordering and scheduling puzzles ask you to rank people (by height, marks, age) or place them in time slots (days, floors, periods). They are seating arrangements in one dimension and reward a systematic grid.
Key concepts
Ranking puzzles
Turn each comparison into an inequality: 'A is taller than B' → A > B. Chain them: A > B, B > C ⇒ A > C. A single definite clue ('D is the tallest') fixes one end.
Scheduling grids
Draw a table with slots (Monday–Friday, floors 1–5) as columns. Fill:
- fixed assignments ('C on Wednesday');
- 'immediately after/before' pairs as blocks;
- 'exactly one day between' pairs (two possible placements each);
- negative clues ('not on Monday') to remove options.
Rank from both ends
If someone is k-th from the top and m-th from the bottom, there are k + m − 1 people. If A is 7th from the left and B 10th from the right, and they swap … use the same formula.
Floors
The ground floor is usually floor 1 in these puzzles – read the instruction. 'Above' means any higher floor; 'immediately above' means the next one.
- Total = rank from top + rank from bottom − 1
- A > B and B > C ⇒ A > C
- 'Exactly one between' → positions differ by 2
Solved examples
Example 1
Among five friends: T is not the oldest. T is older than S. P is younger than T. U is younger than P. U is older than S. Who is the second oldest?
(a) S (b) T (c) U (d) V
- Chain the comparisons into a single order (oldest first): V > T > P > U > S.
- The second oldest is T.
Answer: (b) T
Example 2
Among five friends: S is not the oldest. Q is the oldest. V is younger than R. S is younger than V. V is younger than T. T is younger than R. Who is the oldest?
(a) Q (b) V (c) S (d) R
- Chain the comparisons into a single order (oldest first): Q > R > T > V > S.
- The oldest is Q.
Answer: (a) Q
Example 3
Five guest lectures by L, N, J, O and K are held one per day from Monday to Friday. There is exactly one day between N and K. J has the lecture on Thursday. O is not on Tuesday. J is on the day immediately after K. N is on some day before J. Who lectures on Monday?
(a) L (b) K (c) O (d) N
- Fixed days first, then blocks; the only schedule meeting every clue: Mon – N, Tue – L, Wed – K, Thu – J, Fri – O.
Answer: (d) N
Example 4
Among five friends: T is older than U. T is older than V. S is older than T. R is younger than S. R is older than T. U is older than V. Who is the oldest?
(a) V (b) R (c) S (d) U
- Chain the comparisons into a single order (oldest first): S > R > T > U > V.
- The oldest is S.
Answer: (c) S
Example 5
Among five friends: R is lighter than T. R is lighter than V. T is lighter than U. Q is lighter than R. V is not the heaviest. V is heavier than T. Who is the heaviest?
(a) R (b) U (c) T (d) Q
- Chain the comparisons into a single order (heaviest first): U > V > T > R > Q.
- The heaviest is U.
Answer: (b) U
Example 6
Among five friends: T is older than V. T is older than R. P is younger than R. U is older than R. V is younger than R. T is older than U. P is older than V. Who is the oldest?
(a) T (b) R (c) P (d) V
- Chain the comparisons into a single order (oldest first): T > U > R > P > V.
- The oldest is T.
Answer: (a) T
Example 7
Among five friends: Q is not the oldest. S is the oldest. P is older than R. T is younger than R. R is older than Q. T is older than Q. Who is the third oldest?
(a) Q (b) P (c) R (d) S
- Chain the comparisons into a single order (oldest first): S > P > R > T > Q.
- The third oldest is R.
Answer: (c) R
Example 8
Five guest lectures by O, J, P, L and N are held one per day from Monday to Friday. P is not on Tuesday. P is not on Monday. L has the lecture on Tuesday. J is on the day immediately after N. There is exactly one day between O and P. Who lectures on Thursday?
(a) N (b) P (c) O (d) J
- Fixed days first, then blocks; the only schedule meeting every clue: Mon – O, Tue – L, Wed – P, Thu – N, Fri – J.
Answer: (a) N
- Write comparisons as a single chain with > signs.
- Place blocks before single people.
- If two cases survive, look at what the question asks – sometimes both give the same answer.
- Treating 'taller than B' as 'immediately taller than B'.
- Counting the gap wrongly in 'two people between'.
- Assuming days run Sunday–Saturday when the puzzle says Monday–Friday.
Practice set
Attempt all 12 questions (about 90 seconds each), then check the worked solutions below.
Q1. Among five friends: P is younger than V. Q is older than P. U is the oldest. S is older than Q. V is younger than Q. Who is the third oldest?
(a) Q (b) V (c) U (d) S
Q2. Five guest lectures by L, J, M, N and K are held one per day from Monday to Friday. J has the lecture on Friday. There is exactly one day between M and K. N is not on Thursday. K is on some day before L. K is on the day immediately after N. N has the lecture on Monday. Who lectures on Wednesday?
(a) K (b) L (c) M (d) N
Q3. Among five friends: P is younger than S. R is older than Q. R is the oldest. Q is younger than T. Q is younger than P. T is younger than S. P is younger than T. Who is the second oldest?
(a) Q (b) P (c) T (d) S
Q4. Five guest lectures by M, L, N, O and J are held one per day from Monday to Friday. M is not on Monday. J has the lecture on Tuesday. L has the lecture on Monday. O is not on Wednesday. There is exactly one day between J and M. Who lectures on Tuesday?
(a) O (b) J (c) M (d) L
Q5. Among five friends: Q is lighter than T. T is the heaviest. P is heavier than U. P is heavier than S. Q is heavier than P. U is heavier than S. Who is the second heaviest?
(a) T (b) P (c) Q (d) U
Q6. Among five friends: S is shorter than Q. V is taller than R. V is taller than S. S is taller than T. V is not the tallest. R is shorter than S. T is shorter than R. Who is the third tallest?
(a) T (b) Q (c) R (d) S
Q7. Five guest lectures by L, O, J, N and M are held one per day from Monday to Friday. J is not on Thursday. J has the lecture on Tuesday. M is not on Wednesday. M has the lecture on Friday. L is not on Thursday. L is not on Wednesday. N is on the day immediately after J. Who lectures on Thursday?
(a) N (b) O (c) L (d) J
Q8. Five guest lectures by M, P, N, K and L are held one per day from Monday to Friday. P is on some day before N. N is not on Friday. L is not on Monday. There is exactly one day between P and N. P is on some day before M. M has the lecture on Thursday. L is on the day immediately after P. Who lectures on Monday?
(a) M (b) N (c) P (d) L
Q9. Among five friends: T is taller than S. T is shorter than U. V is shorter than T. V is shorter than R. R is shorter than U. S is taller than V. S is taller than R. Who is the third tallest?
(a) S (b) R (c) U (d) V
Q10. Among five friends: U is lighter than V. U is lighter than T. U is lighter than R. S is lighter than T. T is the heaviest. S is heavier than V. R is lighter than V. Who is the second heaviest?
(a) T (b) V (c) R (d) S
Q11. Five guest lectures by L, P, K, O and M are held one per day from Monday to Friday. L is on some day before M. P has the lecture on Friday. K is not on Tuesday. P is on the day immediately after M. L has the lecture on Wednesday. Who lectures on Monday?
(a) P (b) M (c) K (d) O
Q12. Among five friends: U is the oldest. Q is older than V. Q is older than T. S is younger than Q. V is older than T. V is younger than S. Who is the oldest?
(a) U (b) T (c) S (d) Q
Q1 – (a) Q. Chain the comparisons into a single order (oldest first): U > S > Q > V > P. The third oldest is Q.
Q2 – (b) L. Fixed days first, then blocks; the only schedule meeting every clue: Mon – N, Tue – K, Wed – L, Thu – M, Fri – J.
Q3 – (d) S. Chain the comparisons into a single order (oldest first): R > S > T > P > Q. The second oldest is S.
Q4 – (b) J. Fixed days first, then blocks; the only schedule meeting every clue: Mon – L, Tue – J, Wed – N, Thu – M, Fri – O.
Q5 – (c) Q. Chain the comparisons into a single order (heaviest first): T > Q > P > U > S. The second heaviest is Q.
Q6 – (d) S. Chain the comparisons into a single order (tallest first): Q > V > S > R > T. The third tallest is S.
Q7 – (b) O. Fixed days first, then blocks; the only schedule meeting every clue: Mon – L, Tue – J, Wed – N, Thu – O, Fri – M.
Q8 – (c) P. Fixed days first, then blocks; the only schedule meeting every clue: Mon – P, Tue – L, Wed – N, Thu – M, Fri – K.
Q9 – (a) S. Chain the comparisons into a single order (tallest first): U > T > S > R > V. The third tallest is S.
Q10 – (d) S. Chain the comparisons into a single order (heaviest first): T > S > V > R > U. The second heaviest is S.
Q11 – (c) K. Fixed days first, then blocks; the only schedule meeting every clue: Mon – K, Tue – O, Wed – L, Thu – M, Fri – P.
Q12 – (a) U. Chain the comparisons into a single order (oldest first): U > Q > S > V > T. The oldest is U.
- Comparisons → chain with >
- Grid: fixed, blocks, gaps, negatives
- k + m − 1 people
- Check uniqueness
