Relationships, Ordering and Arrangement Puzzles Short Notes for GATE CS
Relationships, Ordering and Arrangement Puzzles short notes for GATE CS: 4 study cards covering concepts, formulas, shortcuts and exam traps, plus solved prac
relationships ordering and arrangement puzzles short notes
Family Relationships Quick Revision Checklist
Quick Revision Checklist
Build Complete Tree: Always draw full tree before answering.
Standard Symbols: Squares for males, circles for females.
Generation Lines: Place people on correct horizontal lines.
Gender Indicators: Look for explicit terms, don't assume from names.
"Only" vs "Is": Distinguish between "is daughter" and "only daughter".
Paternal: Father's Side|Maternal: Mother's Side|In-law: Marriage
Spatial Placement Quick Revision
Spatial Placement Quick Revision
Draw the Geometry: Never solve mentally.
List Slots: Identify all possible positions (vertices, mid-points).
Identify Anchors: Find parallel lines, diagonals, or centers.
Place Constraints First: Fix variables with unique positions.
Corner Rule: Remember corners belong to two sides.
Elimination: Use "cannot be" clues to remove options.
Verification: Check final map against all original statements.
Memory Hook
Parallel→ Mid-segments
Opposite→ Across center/side
Adjacent→ Touching
Ordering and Ranking Quick Revision
Ordering and Ranking Quick Revision
Draw the Diagram: Linear line with slots.
Absolute vs Relative: Convert all clues to absolute ranks.
Golden Formula:N=L+R−1.
Between Count:(High−Low)−1.
Immediate vs Non-Immediate: Check for gaps.
Overlap Problems: Check both cases.
Verification: Check final sequence against all statements.
Memory Hook
Left + Right - 1→ Total
Immediate→ No Gap
Between→ Exclude Ends
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Question 1
Level 1: Warm-up
In a row of students, M is standing 6th from the left end. N is standing 4 places to the right of M. What is N's position from the left end?
Question 2
Level 1: Warm-up
Five students P, Q, R, S, T have distinct heights. It is known that P is taller than Q, R is taller than S, T is taller than P, and R is taller than T. What is the minimum number of students who are definitely shorter than T?
Question 3
Level 1: Warm-up
In a row of students, A is 8th from the left end and 12th from the right end. Which of the following total counts is IMPOSSIBLE for this row?
Question 4
Level 1: Warm-up
Four students P, Q, R, S have distinct heights. It is known that P is shorter than Q, R is taller than S, and Q is shorter than S. Which of the following statements MUST be true?
Question 5
Level 1: Warm-up
In a row of students, M is 8th from the left end. N is standing to the right of M with at most 5 students between them. What is the maximum possible position of N from the left end?
Question 6
Level 1: Warm-up
In a straight line of 30 students, Ravi stands 12th from the left end. How many students are standing to the right of Ravi?
Question 7
Level 1: Warm-up
In a row of students, A is 7th from the left end and B is 9th from the right end. There are exactly 3 students between A and B. What is the minimum possible number of students in the row?
Question 8
Level 1: Warm-up
According to the rules for avoiding traps in relationship puzzles, if a statement says "P is the son of Q", what is the minimum number of children Q must have?
Question 9
Level 1: Warm-up
Points are placed at all three corners and all three mid-points of a triangle. What is the minimum number of points that lie on at least two different sides of the triangle?
Question 10
Level 1: Warm-up
In a ranking of 5 students by height, A is the shortest. B is taller than only one student. C is taller than D but is not the tallest. How many students are strictly taller than D?
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Relationships, Ordering and Arrangement Puzzles Short Notes for GATE CS
Relationships, Ordering and Arrangement Puzzles short notes for GATE CS: 4 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.
Family Relationships Quick Revision Checklist
Quick Revision Checklist
Build Complete Tree: Always draw full tree before answering.
Standard Symbols: Squares for males, circles for females.
Generation Lines: Place people on correct horizontal lines.
Gender Indicators: Look for explicit terms, don't assume from names.
"Only" vs "Is": Distinguish between "is daughter" and "only daughter".
Paternal: Father's Side|Maternal: Mother's Side|In-law: Marriage
Spatial Placement Quick Revision
Spatial Placement Quick Revision
Draw the Geometry: Never solve mentally.
List Slots: Identify all possible positions (vertices, mid-points).
Identify Anchors: Find parallel lines, diagonals, or centers.
Place Constraints First: Fix variables with unique positions.
Corner Rule: Remember corners belong to two sides.
Elimination: Use "cannot be" clues to remove options.
Verification: Check final map against all original statements.
Memory Hook
Parallel→ Mid-segments
Opposite→ Across center/side
Adjacent→ Touching
Ordering and Ranking Quick Revision
Ordering and Ranking Quick Revision
Draw the Diagram: Linear line with slots.
Absolute vs Relative: Convert all clues to absolute ranks.
Golden Formula:N=L+R−1.
Between Count:(High−Low)−1.
Immediate vs Non-Immediate: Check for gaps.
Overlap Problems: Check both cases.
Verification: Check final sequence against all statements.
Memory Hook
Left + Right - 1→ Total
Immediate→ No Gap
Between→ Exclude Ends
Exam Readiness Checklist
Exam Readiness Checklist
Verify Totals
Ensure the sum of all row requirements equals the sum of all column requirements before starting.
Target Extremes
Begin deduction with rows or columns requiring zero or the maximum possible shaded cells.
Mark Empties
Clearly mark cells that must remain empty (e.g., with a small dot or cross) to prevent re-evaluation and reveal new forced moves.
Option Elimination
In multiple-choice formats, instantly discard any option that fails to meet even a single row or column count. Do not waste time fully solving the grid if an option can be eliminated in one step.
Relationships, Ordering and Arrangement Puzzles: Solved Questions with Step-by-Step Explanations (10 Problems)
Question 1 · Analytical AptitudeMCQ
In a row of students, M is standing 6th from the left end. N is standing 4 places to the right of M. What is N's position from the left end?
A.
9
B.
10
C.
11
D.
8
Correct Answer:
B
Step-by-Step Solution
Key idea: "Places to the right" means you add to the position. This is a direct translation from language to math.
Step 1: M's position from left = 6.
Step 2: N is 4 places to the right of M.
Step 3: N's position from left = M's position + 4
= 6 + 4
= 10.
Note: We add 4 directly because "4 places to the right" means moving 4 positions forward, not counting the spaces between.
Answer: 10
Question 2 · Analytical AptitudeMCQ
Five students P, Q, R, S, T have distinct heights. It is known that P is taller than Q, R is taller than S, T is taller than P, and R is taller than T. What is the minimum number of students who are definitely shorter than T?
A.
1
B.
2
C.
3
D.
4
Correct Answer:
B
Step-by-Step Solution
Key idea: Convert the verbal comparisons to inequalities and determine who is definitely shorter than T.
Step 1: Translate the given information:
P is taller than Q → P > Q
R is taller than S → R > S
T is taller than P → T > P
R is taller than T → R > T
Step 2: Chain the inequalities:
From T > P and P > Q, we get T > P > Q.
From R > T, we get R > T > P > Q.
We also know R > S, but S's relationship to T, P, Q is unknown.
Step 3: Determine who is definitely shorter than T:
P is shorter than T (T > P) ✓
Q is shorter than T (T > P > Q) ✓
S's relationship to T is unknown (only R > S and R > T are known)
R is taller than T (R > T) ✗
Step 4: Count the students definitely shorter than T: P and Q → 2 students.
Answer: 2
Question 3 · Analytical AptitudeMCQ
In a row of students, A is 8th from the left end and 12th from the right end. Which of the following total counts is IMPOSSIBLE for this row?
A.
19
B.
18
C.
20
D.
17
Correct Answer:
B
Step-by-Step Solution
Key idea: The total number of people in a row is determined by the formula N=L+R−1, where L is position from left and R is position from right.
Step 1: Given L=8 and R=12.
Step 2: Apply the formula:
N=L+R−1=8+12−1=19.
Step 3: The only possible total is 19. Any other value is impossible.
Step 4: Check the options:
19: Possible (correct total)
18: Impossible
20: Impossible
17: Impossible
Since the question asks which is IMPOSSIBLE, and options B, C, D are all impossible, we need to select one. The answer is 18 (option B).
Answer: 18
Question 4 · Analytical AptitudeMCQ
Four students P, Q, R, S have distinct heights. It is known that P is shorter than Q, R is taller than S, and Q is shorter than S. Which of the following statements MUST be true?
A.
R is the tallest
B.
P is the tallest
C.
Q is taller than S
D.
S is the shortest
Correct Answer:
A
Step-by-Step Solution
Key idea: Convert the verbal comparisons into inequalities and chain them to find the complete order.
Step 1: Translate the given information:
P is shorter than Q → P<Q
R is taller than S → S<R
Q is shorter than S → Q<S
Step 2: Chain the inequalities:
From P<Q and Q<S, we get P<Q<S.
From S<R, we extend: P<Q<S<R.
Step 3: Determine the complete order from shortest to tallest:
P, Q, S, R
Step 4: Check each option:
"R is the tallest" → TRUE (R is last in the order)
"P is the tallest" → FALSE (P is shortest)
"Q is taller than S" → FALSE (Q < S)
"S is the shortest" → FALSE (P is shortest)
Answer: R is the tallest
Question 5 · Analytical AptitudeMCQ
In a row of students, M is 8th from the left end. N is standing to the right of M with at most 5 students between them. What is the maximum possible position of N from the left end?
A.
12
B.
13
C.
14
D.
15
Correct Answer:
C
Step-by-Step Solution
Key idea: "At most 5 students between" means the maximum gap is 5, which determines N's maximum position.
Step 1: M is at position 8 from the left.
Step 2: N is to the right of M with at most 5 students between them.
Step 3: If there are exactly 5 students between M and N, then:
N's position = M's position + 5 (students between) + 1 (N itself)
N's position = 8 + 5 + 1 = 14
Step 4: This is the maximum position because "at most 5" means 5 is the upper bound.
Answer: 14
Question 6 · Analytical AptitudeMCQ
In a straight line of 30 students, Ravi stands 12th from the left end. How many students are standing to the right of Ravi?
A.
17
B.
18
C.
19
D.
12
Correct Answer:
B
Step-by-Step Solution
Key idea: If you know the total number and a person's position from one end, you can find how many are on the other side by simple subtraction.
Step 1: Total students = 30.
Step 2: Ravi's position from left = 12th.
Step 3: Students to the right of Ravi = Total - Ravi's position from left
= 30 - 12
= 18.
Note: We do not subtract 1 here because we are counting students to the right of Ravi, not including Ravi himself.
Answer: 18
Question 7 · Analytical AptitudeMCQ
In a row of students, A is 7th from the left end and B is 9th from the right end. There are exactly 3 students between A and B. What is the minimum possible number of students in the row?
A.
11
B.
13
C.
16
D.
19
Correct Answer:
A
Step-by-Step Solution
Key idea: When two people's positions from opposite ends are given with a "between" count, there are two cases: they don't overlap, or they overlap.
Step 1: A is 7th from left, B is 9th from right, 3 students between them.
Step 2: Case 1 — A and B do not overlap (A is to the left of B):
Total = (Position of A from left) + (Position of B from right) + (Students between)
Total = 7 + 9 + 3 = 19
Step 3: Case 2 — A and B overlap (A is to the right of B):
Total = (Position of A from left) + (Position of B from right) - (Students between) - 2
Total = 7 + 9 - 3 - 2 = 11
The −2 accounts for A and B being counted twice in the overlap.
Step 4: The minimum possible total is 11.
Answer: 11
Question 8 · Analytical AptitudeMCQ
According to the rules for avoiding traps in relationship puzzles, if a statement says "P is the son of Q", what is the minimum number of children Q must have?
A.
0
B.
1
C.
2
D.
3
Correct Answer:
B
Step-by-Step Solution
Key idea: This is a logical minimum question. The trap is assuming "is the son" implies "is the only son".
Step 1: Analyze the statement "P is the son of Q".
Step 2: This confirms that at least one male child (P) exists.
Step 3: The statement does not use the word "only", so there could be more children, but there must be at least P.
Step 4: The minimum number of children Q must have is exactly 1 (P himself).
Answer: B
Question 9 · Analytical AptitudeMCQ
Points are placed at all three corners and all three mid-points of a triangle. What is the minimum number of points that lie on at least two different sides of the triangle?
A.
2
B.
3
C.
4
D.
6
Correct Answer:
B
Step-by-Step Solution
Key idea: A corner is the intersection of two sides, so it belongs to both sides. A mid-point lies on exactly one side.
Step 1: Identify the six points — three corners (C1, C2, C3) and three mid-points (M1, M2, M3).
Step 2: Determine how many sides each point belongs to:
Each corner is on exactly 2 sides (the two sides that meet at that corner).
Each mid-point is on exactly 1 side (the side it divides).
Step 3: Count points on at least two sides:
Corners: 3 points, each on 2 sides → all 3 qualify.
Mid-points: 3 points, each on 1 side → none qualify.
Step 4: Total = 3 points.
Answer: 3
Question 10 · Analytical AptitudeMCQ
In a ranking of 5 students by height, A is the shortest. B is taller than only one student. C is taller than D but is not the tallest. How many students are strictly taller than D?
A.
1
B.
2
C.
3
D.
4
Correct Answer:
B
Step-by-Step Solution
Key idea: Anchor the extremes first, then arrange the remaining elements.
Step 1: A is the shortest, so A is at position 1.
Step 2: B is taller than only one student, so B is at position 2.
Step 3: The remaining positions are 3, 4, 5 for C,D,E.
Step 4: C is taller than D, and C is not the tallest (not 5). Thus, E must be 5th, C is 4th, and D is 3rd.
Step 5: Students taller than D (position 3) are those at positions 4 and 5. There are 2 such students.