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    Relationships, Ordering and Arrangement Puzzles PYQs for GATE CS

    Solve 5+ Relationships, Ordering and Arrangement Puzzles previous year questions for GATE CS with answers and detailed solutions. Free sample questions below.

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    Question 1
    2026 Slot Set2 PYQ
    Level 3: Exam Standard
    The figure in Panel I below is a grid of cells with four rows and four columns. The numbers on the top and on the left represent the number of cells that are to be shaded in that column and row, respectively. Which one of the options shown in Panel II below represents the grid shaded correctly?
    Panel I Panel II 2 2 2 2 3 1 2 2 (i) (ii) (iii) (iv)
    Question 2
    2026 Slot Set1 PYQ
    Level 3: Exam Standard
    In the 2020 summer Olympics’ Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were six rounds of throws with each athlete having one throw per round. The best of all the throws of each athlete is considered for the medal. Following were the observations about the throws:

    i. The first and second rounds were dominated by Neeraj Chopra with a gold medal performance in his second throw, while the other two athletes did not have any medal winning throws in these rounds.

    ii. The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.

    iii. After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.

    iv. In the fourth round, the throw by Jakub Vadlejch was the best in that round.

    In which round did Vitezlav Vesely have his best throw?
    Question 3
    2025 Slot Set1 PYQ
    Level 3: Exam Standard
    Consider the relationships among P, Q, R, S, and T:

    • P is the brother of Q.
    • S is the daughter of Q.
    • T is the sister of S.
    • R is the mother of Q.

    The following statements are made based on the relationships given above.

    (1) R is the grandmother of S.

    (2) P is the uncle of S and T.

    (3) R has only one son.

    (4) Q has only one daughter.

    Which one of the following options is correct?
    Question 4
    2022 PYQ
    Level 3: Exam Standard
    The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:

    • The line joining P and R is parallel to the line joining Q and S.
    • P is placed on the side opposite to the corner T.
    • S and U cannot be placed on the same side.

    Which one of the following statements is correct based on the above information?
    Question 5
    2021 Slot Set2 PYQ
    Level 3: Exam Standard
    Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.

    Observation I: S is taller than R.

    Observation II: Q is the shortest of all.

    Observation III: U is taller than only one student.

    Observation IV: T is taller than S but is not the tallest.

    The number of students that are taller than R is the same as the number of students shorter than ______.
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    Relationships, Ordering and Arrangement Puzzles PYQs for GATE CS

    Solve 5+ Relationships, Ordering and Arrangement Puzzles previous year questions for GATE CS with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Relationships, Ordering and Arrangement Puzzles

    Chapter Roadmap

    Relationships, Ordering & Arrangement Puzzles

    Topic 1 Family & Blood Relationships
    Topic 2 Spatial & Geometric Arrangements
    Topic 3 Ordering, Ranking & Sequences
    Topic 4 Grid Shading & Constraints
    How to use: Start with Topic 1 to build your foundation. Each subsequent topic builds on these skills. Speed comes from systematic approach, not memorization.

    Family and Blood Relationships

    Foundation Topic

    Family and Blood Relationships

    Decode complex family connections to determine how people are related.
    • The fundamental family structure and generational levels
    • Relationship terminology (paternal, maternal, in-laws)
    • Building family tree diagrams systematically
    • Inferring indirect relationships from given information
    • Avoiding common traps in relationship puzzles

    Relationships, Ordering and Arrangement Puzzles: Solved Questions with Step-by-Step Explanations (5 Problems)

    Question 1 · Analytical Aptitude · 2026_Set2 MCQ
    The figure in Panel I below is a grid of cells with four rows and four columns. The numbers on the top and on the left represent the number of cells that are to be shaded in that column and row, respectively. Which one of the options shown in Panel II below represents the grid shaded correctly?
    Panel I Panel II 2 2 2 2 3 1 2 2 (i) (ii) (iii) (iv)
    1. A.

      (i)

    2. B.

      (ii)

    3. C.

      (iii)

    4. D.

      (iv)

    Correct Answer:

    B

    Step-by-Step Solution

    Insight: Verify total row and column sums first, then use forced moves starting with the most constrained row or column.

    Exam route: Row sums = 3 + 1 + 2 + 2 = 8. Column sums = 2 + 2 + 2 + 2 = 8. Consistency check passed. Row 2 requires exactly 1 shaded cell. Inspecting the options: Option (i) has 2 shaded in Row 2 (invalid). Option (iii) has 2 shaded in Row 2 (invalid). Option (ii) has 1 shaded in Row 2. Verify Option (ii) columns: Col 1 has 2, Col 2 has 2, Col 3 has 2, Col 4 has 2. All constraints satisfied. Option (ii) is correct.

    Learning route:

    Step 1: Consistency Check. Sum of row requirements (3+1+2+2 = 8) must equal sum of column requirements (2+2+2+2 = 8). They match.

    Step 2: Identify Extremes. Row 2 requires only 1 shaded cell out of 4. This is the tightest constraint.

    Step 3: Option Elimination. Instead of solving the grid from scratch (which is time-consuming), evaluate the given options against the tightest constraint.

    Step 4: Check Row 2 in all options. Option (i) shows 2 shaded cells. Option (iii) shows 2 shaded cells. Both are immediately discarded.

    Step 5: Verify the survivor. Option (ii) has exactly 1 shaded cell in Row 2. Now verify its columns: Col 1 (Rows 1, 4) = 2. Col 2 (Rows 2, 4) = 2. Col 3 (Rows 1, 3) = 2. Col 4 (Rows 1, 3) = 2. All column sums are exactly 2. Option (ii) is the unique valid configuration.

    Question 2 · Analytical Aptitude · 2026_Set1 MCQ
    In the 2020 summer Olympics’ Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were six rounds of throws with each athlete having one throw per round. The best of all the throws of each athlete is considered for the medal. Following were the observations about the throws:

    i. The first and second rounds were dominated by Neeraj Chopra with a gold medal performance in his second throw, while the other two athletes did not have any medal winning throws in these rounds.

    ii. The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.

    iii. After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.

    iv. In the fourth round, the throw by Jakub Vadlejch was the best in that round.

    In which round did Vitezlav Vesely have his best throw?
    1. A.

      Third

    2. B.

      Fourth

    3. C.

      Fifth

    4. D.

      Sixth

    Correct Answer:

    A

    Step-by-Step Solution

    Insight: Vitezlav's best throw must be a medal-winning throw, eliminating rounds where he had no medal-winning throws or fouled.

    Exam route: Clue (i) eliminates rounds 1 and 2. Clue (ii) eliminates round 6. Clue (iii) states that after 4 rounds, he could not improve in succeeding rounds, meaning his best throw was already locked in by round 4. Clue (iv) states Jakub had the best throw in round 4. Thus, Vitezlav's best throw must have occurred in round 3.

    Learning route:

    Step 1: Identify the goal: find the round of Vitezlav's best throw.

    Step 2: Apply Clue (i): Rounds 1 and 2 are eliminated for Vitezlav.

    Step 3: Apply Clue (ii): Round 6 is eliminated (foul).

    Step 4: Apply Clue (iii): "After four rounds... could not improve in succeeding rounds" implies his best throw was established in or before round 4, and rounds 5 and 6 were worse. This eliminates round 5.

    Step 5: Apply Clue (iv): Jakub had the best throw in round 4. While Vitezlav could theoretically have his best in round 4, the phrasing "after four rounds... could not improve" strongly implies the peak was already reached prior, making round 3 the only logically consistent choice that satisfies all constraints without contradiction.

    Question 3 · Analytical Aptitude · 2025_Set1 MCQ
    Consider the relationships among P, Q, R, S, and T:

    • P is the brother of Q.
    • S is the daughter of Q.
    • T is the sister of S.
    • R is the mother of Q.

    The following statements are made based on the relationships given above.

    (1) R is the grandmother of S.

    (2) P is the uncle of S and T.

    (3) R has only one son.

    (4) Q has only one daughter.

    Which one of the following options is correct?
    1. A.

      Both (1) and (2) are true.

    2. B.

      Both (1) and (3) are true.

    3. C.

      Only (3) is true.

    4. D.

      Only (4) is true.

    Correct Answer:

    A

    Step-by-Step Solution

    Insight: Build a generational family tree using standard symbols (squares for males, circles for females, horizontal lines for spouses/siblings, vertical for parent-child) before evaluating any statement.

    Exam route:

    Step 1: "R is the mother of Q" R (Gen 1, Female) Q (Gen 2).

    Step 2: "P is the brother of Q" P (Gen 2, Male) is sibling of Q.

    Step 3: "S is the daughter of Q" and "T is the sister of S" S, T (Gen 3, Female) are children of Q.

    Step 4: Evaluate statements. (1) R is grandmother of S: True (R is mother of Q, Q is parent of S). (2) P is uncle of S and T: True (P is brother of Q, Q is parent of S, T). (3) R has only one son: Unknown (Q's gender is not specified, and R could have other children). (4) Q has only one daughter: False (Q has at least two daughters, S and T).

    Step 5: Select "Both (1) and (2) are true."

    Learning route:

    Step 1: Draw Gen 1: R (Female, circle).

    Step 2: Draw Gen 2: P (Male, square) and Q (gender unknown) connected horizontally (siblings), with a vertical line from R.

    Step 3: Draw Gen 3: S and T (Females, circles) connected horizontally (sisters), with a vertical line from Q.

    Step 4: Trace paths for evaluation. Path R Q S confirms R is grandmother. Path P Q S,T confirms P is uncle.

    Step 5: Identify "Unknown" traps. "Only one son" requires explicit confirmation of all children and their genders, which is absent.

    Question 4 · Analytical Aptitude · 2022 MCQ
    The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:

    • The line joining P and R is parallel to the line joining Q and S.
    • P is placed on the side opposite to the corner T.
    • S and U cannot be placed on the same side.

    Which one of the following statements is correct based on the above information?
    1. A.

      P cannot be placed at a corner

    2. B.

      S cannot be placed at a corner

    3. C.

      U cannot be placed at a mid-point

    4. D.

      R cannot be placed at a corner

    Correct Answer:

    B

    Step-by-Step Solution

    Insight: In a triangle, the only way two lines formed by {corners, midpoints} are parallel is if one is a mid-segment (connecting two midpoints) and the other is the side parallel to it (connecting two corners).

    Exam route:

    Step 1: PR || QS. This means either {P, R} are midpoints and {Q, S} are corners, OR {P, R} are corners and {Q, S} are midpoints.

    Step 2: "P is placed on the side opposite to the corner T." This implies T is a corner, and the side containing P is opposite to T.

    Step 3: Test Case A: {P, R} are midpoints. Then PR is a mid-segment. It is parallel to the side connecting the two corners not on the sides of P and R. For QS to be parallel to PR, Q and S must be those two corners. Thus, corners = {Q, S, T}. This leaves {P, R, U} as midpoints. But S is a corner, so it belongs to two sides. U is a midpoint, so it must lie on one of those two sides, violating "S and U cannot be placed on the same side". Contradiction.

    Step 4: Test Case B: {P, R} are corners. Then PR is a side. For QS to be parallel to PR, QS must be the mid-segment. Thus, {Q, S} are midpoints. This perfectly satisfies all clues: T is the third corner, and S (a midpoint) and U (the remaining midpoint) are on different sides.

    Step 5: Conclusion: S must be a midpoint. Therefore, "S cannot be placed at a corner" is definitively true.

    Learning route:

    Step 1: Recall the geometric constraint: Parallel lines in this context require one mid-segment and one side.

    Step 2: Set up the two mutually exclusive cases for {P, R} and {Q, S}.

    Step 3: Use the "opposite to corner T" clue to anchor T as a corner and link P to a specific side.

    Step 4: Apply the negative constraint "S and U not on same side" to eliminate the case where S is a corner (as it would force U onto a side touching S).

    Step 5: Deduce that S must be a midpoint, making the statement "S cannot be placed at a corner" the correct answer.

    Question 5 · Analytical Aptitude · 2021_Set2 MCQ
    Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.

    Observation I: S is taller than R.

    Observation II: Q is the shortest of all.

    Observation III: U is taller than only one student.

    Observation IV: T is taller than S but is not the tallest.

    The number of students that are taller than R is the same as the number of students shorter than ______.
    1. A.

      T

    2. B.

      R

    3. C.

      S

    4. D.

      P

    Correct Answer:

    C

    Step-by-Step Solution

    Insight: Anchor the extremes (shortest, tallest) first, then chain the relative inequalities to build the complete order.

    Exam route: Q is shortest (Rank 1). U is taller than only one (Rank 2). Remaining: P, R, S, T for Ranks 3, 4, 5, 6. We know T > S > R. Since T is not the tallest, P must be Rank 6 (tallest). This forces T = 5, S = 4, R = 3. Students taller than R (Ranks 4, 5, 6) = 3. Students shorter than S (Ranks 1, 2, 3) = 3. Match is S.

    Learning route:

    Step 1: Assign absolute ranks to extremes. Q = 1 (shortest). U = 2 (taller than only Q).

    Step 2: Identify the remaining pool: {P, R, S, T} for ranks {3, 4, 5, 6}.

    Step 3: Chain the relative clues: T > S and S > R T > S > R.

    Step 4: Apply the negative constraint: "T is not the tallest". Since T > S > R, T must be at least Rank 4. If T were Rank 6, it would be the tallest. Thus, P must be Rank 6.

    Step 5: Fill the remaining slots: T = 5, S = 4, R = 3.

    Step 6: Answer the specific query. Taller than R (Ranks 4, 5, 6 S, T, P) is 3 students. We need someone with exactly 3 students shorter than them. S (Rank 4) has Ranks 1, 2, 3 (Q, U, R) shorter than them. Count = 3. Match confirmed.

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