7.3 Analytical Reasoning & Puzzles

Why Puzzles Carry Weight

Puzzles are the heart of analytical reasoning and account for a sizeable chunk of the 30-mark Reasoning section. They reward methodical deduction over guesswork: every clue either fixes a variable or eliminates a possibility, and once the grid is half-filled the remaining cells fall by elimination. RRB Group D puzzles stay Class-10 level — usually 4–6 entities with 2–3 attributes — so the key is speed built on a reliable template.

The Grid Method

1. List entities on rows (people, cities, animals).
2. List attributes on columns (floor, subject, colour, car).
3. Mark definites with ✓ and impossibles with ✗ as you read each clue.
4. Propagate: if a row has only one open cell, that cell must be the remaining value; if a column has only one open cell, fill the row.
5. Re-read the clues once the grid is half-full — conditional clues that were unusable earlier may now bite.

Linear Seating Arrangement

People sit in a row facing one direction. Clues give positions ("A sits at one of the extreme ends") or relations ("B sits second to the left of C").

Worked Example 1 — Linear Seating

Question: Five friends A, B, C, D, E sit in a row facing North. A sits second from the left end. B is an immediate neighbour of A. C sits to the immediate right of D. E sits at one of the extreme ends. Who sits at the right end?

Step 1 — Set positions 1 to 5 (left to right, all facing North).

Step 2 — Place A. "A sits second from the left end" → A is in position 2.

Step 3 — Place B. B is an immediate neighbour of A. The neighbours of position 2 are positions 1 and 3. So B is in position 1 or 3.

Step 4 — Place E at an extreme end. Extreme ends are positions 1 and 5.

• If B is in position 1, then E must be in position 5 (since position 1 is taken).
• If B is in position 3, then E could be in position 1 or 5.

Step 5 — Use the C/D clue. "C sits to the immediate right of D." Facing North, the right of D is the position with the next higher number, so the order is D → C in consecutive positions.

• Try B in position 1, E in position 5. Remaining positions 3 and 4 must hold D and C. D must be in 3, C in 4 (since C is right of D).
  • Row: B(1), A(2), D(3), C(4), E(5). Check all clues: A in 2 ✓, B adjacent to A ✓, C immediately right of D ✓, E at extreme end ✓.
• The arrangement is B, A, D, C, E.

Answer: E sits at the right end.

Circular Seating Arrangement

People sit around a circular table. The crucial trap: "to the left of X" depends on whether everyone faces the centre or away from the centre.

• If everyone faces the centre, the left of X is the person one seat anticlockwise from X.
• If everyone faces outward (away from centre), the left of X is the person one seat clockwise from X.

Worked Example 2 — Circular Seating

Question: Six people P, Q, R, S, T, U sit around a circular table facing the centre. P sits second to the right of Q. R is an immediate neighbour of both P and S. T sits third to the left of S. Who sits opposite U? (Assume six equally spaced seats.)

Step 0 — Fix the conventions before touching a clue. Draw six seats at the 12, 2, 4, 6, 8 and 10 o'clock positions. Everyone faces the centre, so from any person's point of view right = clockwise and left = anticlockwise. Anchor the first named person, Q, at 12 o'clock; in a circular puzzle only relative positions matter, so fixing one person costs nothing.

Step 1 — P sits second to the right of Q. From Q(12) going clockwise: 2 o'clock is the first seat to Q's right, 4 o'clock is the second. So P is at 4.

Step 2 — R is an immediate neighbour of P. The seats adjacent to 4 are 2 and 6, so R is at 2 or 6. Test both.

• If R is at 2: S must be adjacent to R, so S would be at 12 or 4 — but those are Q and P. Contradiction, so this branch dies.
• If R is at 6: S must be adjacent to R, so S is at 4 (P, taken) or 8. So R is at 6 and S is at 8.

Step 3 — T sits third to the left of S. From S(8) going anticlockwise: 6 (first, R), 4 (second, P), 2 (third). Seat 2 is free, so T is at 2.

Step 4 — Fill the last seat. Only 10 o'clock remains, so U is at 10.

The completed circle, clockwise from 12: Q(12), T(2), P(4), R(6), S(8), U(10). Check every clue against it before answering — P is two seats clockwise from Q ✓, R is next to both P and S ✓, T is three seats anticlockwise from S ✓.

Step 5 — Answer the question asked. "Opposite" on a six-seat circle means three seats away. Opposite U(10) is seat 4, which is P.

Answer: P sits opposite U.

Notice the shape of the method: fix the conventions, anchor one person, then use the branching clue (Step 2) to split into cases and let the contradiction kill the wrong branch. If both branches survive, the puzzle is under-determined and the correct exam answer is "cannot be determined"; if neither survives, you have almost certainly reversed left and right, so redraw before you redo the logic.

Trap: Always sketch the circle and label the facing direction in the margin. Mixing up facing-centre vs facing-outward is the most common circular puzzle error.

Ranking and Ordering

Use the formula for a fully ordered population without ties:

$\text{Total} = (\text{rank from top}) + (\text{rank from bottom}) - 1$

Worked Example 3 — Ranking

Question: In a class of 40, Amit is 7th from the top and Suman is 11th from the bottom. How many students sit between them if Amit is above Suman?

Step 1 — Suman's rank from the top. Total = rank from top + rank from bottom − 1, so 40 = rank from top + 11 − 1 → rank from top = 30. Suman is 30th from the top.

Step 2 — Students between. Positions strictly between 7 and 30: 30 − 7 − 1 = 22.

Answer: 22 students sit between Amit and Suman.

Floor Puzzles

People live on consecutive floors of a small building (typically 5–7 floors). Use the same grid method: rows = people, columns = floor number. "A lives on an odd-numbered floor" eliminates even floors; "B lives above C" fixes relative order.

Scheduling Puzzles

People do tasks on different days of a week. Treat days as positions 1–7 and apply the linear seating method.

Exam trap: RRB sometimes includes a 'not' clause — 'A does not live on the top floor'. Read every word; the 'not' eliminates the top floor and is often the only clue that breaks an otherwise ambiguous puzzle.