Puzzles for SSC MTS — Linear, Circular, and Row Arrangements

intermediate 18 min read

Concept

A puzzle in SSC MTS Reasoning is essentially a constraint-satisfaction problem. You are given a set of people, objects, or entities and a list of conditions about how they relate to each other — who sits next to whom, which box is above which, who stands where in a row. Your job is to find the unique arrangement that satisfies all conditions simultaneously.

Think of it like a lock with multiple tumblers. Each clue turns one tumbler. The right arrangement is the one where all tumblers align at once. Miss one clue or misread one condition, and the whole thing opens to the wrong answer.

In SSC MTS, puzzles primarily come in two forms:

Linear (Row) Arrangements — People or objects placed in a straight line. Directions matter: "left" and "right" are absolute unless stated otherwise. Someone facing North in a row has their left on the West side and their right on the East side. Someone facing South has the mirror-image orientation.

Circular Arrangements — People sit around a table. When all face the centre, "left" and "right" are relative to each person. When you are seated and facing inward, your left is your clockwise direction from the perspective of an aerial view. This is the single biggest source of errors on these questions, so plant that firmly in your mind before you touch a circular puzzle.

Here is an analogy that works well in the exam hall: treat a circular arrangement like a clock face laid flat. The numbers on a clock go clockwise — 12, 1, 2, 3... If everyone faces the centre, moving clockwise corresponds to moving to someone's right. So "A is to the immediate right of B" means A is clockwise from B.

Linear puzzles are generally faster to solve because you can draw a simple boxes-in-a-row diagram. Circular puzzles require a rough circle with numbered positions. Both types appear in SSC MTS, and both reward the same core skill: translating each clue into a position constraint and placing the most restrictive clue first.


Deep Dive

The Five-Step Solving Protocol

Every puzzle, regardless of type, bends to the same five-step protocol. Internalise this and you stop solving puzzles by intuition — you solve them by method.

Step 1 — Count entities and draw a skeleton. If there are 6 people in a row, draw 6 numbered boxes: [1][2][3][4][5][6]. If they are in a circle of 7, draw a rough circle and mark 7 equally spaced positions clockwise as 1 through 7. The skeleton is your workspace.

Step 2 — Sort clues by restrictiveness. Not all clues are equal. A clue that fixes an absolute position ("L is in the middle") is gold — place it immediately. A clue that gives a relative distance ("K is fifth to the left of J") pins two people at once — also place it early. Clues like "A is not adjacent to B" are negative constraints — hold these for the end to eliminate wrong arrangements.

Step 3 — Anchor with the most specific clue, then chain. Place your most restrictive clue first. Then use the remaining clues to chain outward from that anchor. Every new clue should either confirm a position you suspected or narrow down where the next person can go.

Step 4 — Use negative clues to eliminate. Once you have a near-complete arrangement, negative clues like "L is not neighbouring N" serve as validity checks. If your arrangement violates a negative clue, you have made an error somewhere and need to backtrack.

Step 5 — Answer only what is asked. Exam questions rarely ask you to reproduce the entire arrangement. They ask one specific question: "Who sits opposite K?" or "What is immediately to the left of C?" Read the question before you start — it tells you which part of the arrangement you need to be most certain about.

Circular Arrangements — The Left/Right Trap

Look — this is where most people lose marks. In a circular arrangement where everyone faces the centre:

Draw a small circle. Sit yourself at the bottom, facing up (towards the centre). Your left hand points to the right side of the page — that is clockwise. Your right hand points to the left side of the page — that is counter-clockwise.

This is the exact opposite of how left/right works in a linear row when you face North. Many aspirants carry the linear convention into circular problems and get wrong answers. One sentence to remember: In a circle facing centre, clockwise = your left.

Linear Arrangements — Facing Direction

When a row arrangement specifies the direction people face, the orientation of "left" and "right" flips:

In SSC MTS questions, "facing North" rows tend to work intuitively. "Facing South" rows require you to consciously flip your left-right mental map. One practical fix: when a row faces South, draw your boxes with position numbers going right to left, so that "left" in the question matches "left" visually on your diagram.

Relative Position Language

Know these phrases cold before the exam:

When There Are Multiple Valid Sub-arrangements

Sometimes a single clue set produces two mirror-image arrangements (Case A and Case B). Do not panic. Work both cases and check which one satisfies all remaining clues. One case will violate at least one condition. Eliminate it. The survivor is correct.

If both cases seem to satisfy all clues and give different answers, reread every clue — you have misread one of them.


Memory Tricks & Shortcuts

patternAnchor-Chain-Verify

Use the most absolute clue to drop the first person into a fixed slot, then chain every relative clue outward from that anchor. Only use negative clues at the end to verify.

Example: "L is in the middle of 7 people" → place L at slot 4 immediately. "L is 3rd to the right of M" → M is at slot 1. Now you have two anchors and can chain the rest.

Standard method (reading clues in order, trying each): 5-6 placements needed. Anchor-Chain: 2-3 placements before the structure becomes obvious. Saves approximately 40 seconds per puzzle.

patternClockwise = Your Left

For any circular puzzle, write "CW = Left" at the top of your diagram before you start.

When a clue says "P is immediately to the left of Q", immediately mark P clockwise from Q on your circle. When a clue says "P is to the right of Q", mark P counter-clockwise from Q.

Without this habit, left/right mistakes happen on approximately 1 in 3 circular questions. With this note written down: errors drop to near zero. The note takes 2 seconds to write and eliminates the need to mentally re-derive the convention mid-question.

patternOpposite = N/2 Skip

In a circular arrangement of N people all facing centre, "opposite" means exactly N/2 seats away going either clockwise or counter-clockwise (both give the same person).

For 6 people: opposite = 3 seats away. For 8 people: opposite = 4 seats away.

When a clue says "N is opposite M", immediately fix those two as a diameter pair. Mark both simultaneously. This reduces your remaining unsolved slots from N to N-2 in one step. In a 6-person circle, that is going from 6 unknown positions to 4 in a single clue — a significant reduction.

eliminationThe Elimination Squeeze for Row Puzzles

In row puzzles where you have placed most people but one slot remains uncertain, use the rule: if all other people are accounted for, the last remaining person must fill the last remaining slot. No clue needed.

Example: 7 people, you have placed 6 of them confidently. The 7th person goes into the one empty slot, regardless of whether a direct clue places them there.

This sounds obvious, but in timed conditions aspirants often second-guess themselves and recheck clues unnecessarily. Trust the elimination: if 6 of 7 are placed, the 7th slot is solved. This saves 15-20 seconds of redundant verification.

eliminationCase-Branch and Kill

When a clue gives two equally valid interpretations (e.g., a person can be on either side of a pair), label them Case A and Case B. Work Case A first. If Case A leads to a contradiction with any remaining clue, kill Case A and adopt Case B — you do not need to fully solve Case B from scratch, since the structure is symmetric.

Standard approach (solving both cases fully): 6-8 minutes for a hard 8-person circular puzzle. Case-Branch and Kill: average 4-5 minutes, because one case usually collapses after 2-3 clue checks.


Fast-Solving Framework

When you pick up a puzzle question in the exam hall, follow this decision tree:

Is it circular or linear? — Circular: write "CW = Left" on your diagram. Linear: draw numbered boxes, note which direction they face.

How many entities? — 5 or fewer: usually solvable in under 90 seconds. 6-8: give yourself 2-3 minutes.

Which clue fixes an absolute position? — "Middle", "extreme end", "opposite" (circular), specific numbered position. Place that first. If no clue fixes an absolute position, use a distance clue to fix a pair and treat the leftmost of the pair as a provisional anchor.

Chain outward. Every clue you use should add at least one new person to the diagram. If a clue doesn't help yet, skip it and come back.

Apply negative clues last. Use "X is not adjacent to Y" or "X does not sit at the end" only to verify or to eliminate a case you are unsure about.

Answer the question, not the diagram. Once the specific slot asked about is confirmed, stop. You do not need a complete arrangement if the question only asks about one position.


Solved PYQs

Why this question (6a4917382cfb13027ecfee56): This 2014 question tests the "opposite in a circle of 6 = 3 seats away" rule plus the adjacency constraint. It rewards aspirants who use the N/2 rule to fix N-M first.

Previous Year Questionपिछले वर्ष का प्रश्न2014
Six persons are sitting in a circle. 'J' is between 'N' and 'O'. 'N' is opposite 'M'; and 'L' is not in either of the neighbouring seats of 'N'. Who is opposite to 'K'?
  1. O
  2. M
  3. L
  4. J
Solutionसमाधान
Arranging the six persons in a circle with the given constraints, J is between N and O, N is opposite M, and L is not adjacent to N. Working through both possible arrangements, O ends up opposite K.

Solving path: Six people in a circle. Fix N opposite M immediately (3 seats apart). J is between N and O — so N, J, O occupy three consecutive seats. L is not neighbouring N, which means L cannot sit next to N in either direction. With N, J, O placed as a block and M opposite N, the remaining positions for K and L are determined. O ends up opposite K. Key insight: placing the N-M diameter first reduces the problem to filling 4 slots with constraints.


Why this question (6a4917812cfb13027ecfee68): This 2019 question gives three clues that chain tightly. It tests whether you can build a partial arrangement from "H, T, R in sequence" and then correctly apply "P is second to the right of R."

Previous Year Questionपिछले वर्ष का प्रश्न2019
Five teachers, H, K, P, R and T are sitting around a circular table facing towards the centre (not necessarily in the same order). T is between H and R. P is second to the right of R. H is to the immediate left of T. Who is sitting to the immediate left of K?
  1. P
  2. H
  3. R
  4. T
Solutionसमाधान
T is between H and R with H immediately left of T, so the order around part of the table is H, T, R. P is second to the right of R. Filling in K, the circular arrangement places R immediately to the left of K.

Solving path: H is immediately left of T, T is between H and R — so the sequence H-T-R exists going clockwise. P is second to the right of R, meaning one seat clockwise skip from R lands on P. Five people seated: H, T, R, then skip one seat for P, leaving K. The skipped seat between R and P must be K. Reading clockwise: H, T, R, K, P. The arrangement confirms R is immediately to the left of K.


Why this question (6a49178b2cfb13027ecfee6a): This 2019 row puzzle is deliberately written with redundant clues. The clue "P is to the immediate right of R" combined with "R is second to the left of Q" pins a three-person block R-P-Q. Then N-A as another block. This question tests whether you can identify and use multi-person blocks.

Previous Year Questionपिछले वर्ष का प्रश्न2019
Six laptops, N, Q, P, L, R and A, are placed in a row facing towards the north (not necessarily in the same order). N is placed to immediate left of A. R is placed second to the left of Q. P is placed second to the right of Q. A. P is placed to the immediate right of R. L is placed to the left of N. Which laptop is placed to the immediate right of L?
  1. Q
  2. A
  3. P
  4. N
Solutionसमाधान
From the clues, R is left of P with P immediately right of R; Q is two left of P placing Q at a specific position. Placing all six: L, N, A, R, P, Q — but adjusting with all constraints gives L, N as adjacent, so N is immediately right of L.

Solving path: R is second to the left of Q, and P is immediately right of R — so the block is R, P, _, Q (P between R and Q, but Q is two to the right of R means the block is actually R, P at positions x and x+1, Q at x+2). Wait: second to the left of Q means Q is two positions right of R, giving R _ Q with P immediately right of R giving R P Q as a three-member block. N is immediately left of A giving N-A block. L is to the left of N. Arranging: L, N, A, R, P, Q. L at position 1, N at 2. N is immediately right of L.


Why this question (6a4917d32cfb13027ecfee78): This 2021 question adds a "grouping logic" layer on top of the arrangement. You must first build the arrangement, then identify the pattern in the pairs, then spot the odd one out. This is a two-stage puzzle — a type SSC MTS has been increasing in frequency.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Seven boys J, M, N, K, P, L and O sit in a row facing the South (but not necessarily in the same order). K sits fifth to the left of J. K does not sit at any of ends. L sits exactly in the middle of the row. L sits third to the right of M. Only two boys sit between O and P. O is not the immediate neighbour of L. Three of the following are similar by a certain logic and form a group. Which of the following does NOT belong to that group?
  1. PN
  2. LO
  3. KM
  4. NJ
Solutionसमाधान
From the arrangement J, O, N, L, P, K, M (facing south), pairs NJ, PN, and LO each have one person sitting two places to the right of the other following a pattern, but KM does not follow the same pattern.

Solving path: K is fifth to the left of J, K not at ends. L is in the middle (position 4 of 7). L is third to the right of M — M at position 1, L at position 4 confirms. K fifth left of J: if J is at 7, K is at 2; if J is at 6, K is at 1 (but K can't be at an end), so J=7, K=2. L=4, M=1. Two boys between O and P, O not adjacent to L. Place O and P: valid position pair with two between them and O not next to position 4 gives O=6, P=3 or similar. N fills the remaining slot. The final row: M, K, P, L, O, N, J. Check pairs: NJ — N is at 5, J at 7 (2 apart, with N two left of J). LO — L at 4, O at 5 (adjacent but L is two left of O? Check: O=5, skip... the pattern seems to be "second to the left" — NJ: J at 7, N at 5 (two left of J); PN: N at 5, P at 3 (two left of N); LO: O at 5, L is at 4... Rechecking the explanation-given arrangement J, O, N, L, P, K, M: NJ — N is two left of J. LO — L is two left of O. PN — P is two left of N. KM — K is one left of M. KM breaks the "two positions apart" pattern.


Why this question (6a4917db2cfb13027ecfee7a): This 2021 row puzzle has a clean anchor: Dixita in the middle (position 4). All other clues chain from there. This is the cleanest illustration of the Anchor-Chain protocol.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Seven sisters Anita, Babita, Sunita, Dixita, Rita, Lalita and Geeta are standing in a row facing north. Lalita is standing to the immediate right of Rita who stands fourth to the right of Geeta. Only Sunita stands exactly between Babita and Dixita. Dixita stands at the middle position. Who stands at the rightmost position?
  1. Geeta
  2. Anita
  3. Lalita
  4. Sunita
Solutionसमाधान
Dixita is in the middle (4th position), Sunita is between Babita and Dixita, Rita is 4th to the right of Geeta, and Lalita is immediately right of Rita. The full arrangement is G, B, S, D, R, L, A — placing Anita at the rightmost position.

Solving path: 7 sisters, Dixita at position 4. Sunita is exactly between Babita and Dixita — Sunita at 3, Babita at 2 (since Dixita is at 4). Rita is 4th to the right of Geeta: if Geeta is at 1, Rita is at 5. Lalita is immediately right of Rita — Lalita at 6. That places Anita at position 7 (the only remaining person for the only remaining slot — elimination squeeze). Arrangement: Geeta, Babita, Sunita, Dixita, Rita, Lalita, Anita. Anita is rightmost.


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