CAT Arrangements and Puzzles: Order the Constraints, Not the People
An arrangement set gives you entities, positions and a list of conditions. Almost every candidate works the conditions in the order printed. That is the single most expensive habit in this question type, because the conditions are not equally powerful and the printed order is not the useful one.
Sort the conditions by how much each one fixes, apply the strongest first, and a set that looked like eight minutes of casework often resolves in three.
"C is in seat 4" beats "A is left of B" every time
A condition that fixes a position outright eliminates most of the possibility space in one move. A relative condition eliminates half of it at best. Working them in the given order means enumerating cases that a later condition would have deleted for free.
Quick Answer (30-Second Read)
First move
Read all, draw none
Then rank conditions
Time budget
8–12 minutes
Hard stop either way
- Rank conditions by strength — fixing, blocking, distance, relative, negative, conditional.
- Draw the frame before any entity: the number of slots, and what each slot means.
- Negative conditions are placed as crosses, not held in your head.
- Two cases is fine; four means you sequenced wrongly. Go back rather than pushing through.
- Circular sets need a fixed reference point before anything else can be placed.
Section structure per the official CAT bulletin at iimcat.ac.in.
CAT Mock Test — arrangements under a closing section
Casework you can afford at home is casework you cannot afford at minute 28. Practise where that is true.
Five structures, and how to spot which you have
| Structure | Signal in the set | Frame to draw |
|---|---|---|
| Linear | A row, a queue, ranks, floors, positions left to right | Numbered slots in a line |
| Circular | A round table, a circle, "facing the centre" | A circle with one position fixed as reference |
| Matrix or grid | Entities to be matched against two or more attributes | A table, entities as rows, attributes as columns |
| Grouping | Entities divided into teams, committees or floors with capacities | Boxes with capacity counts written in |
| Sequencing over time | Days, months, rounds, an order of events | A line of time slots, with the unit stated |
Draw the frame before you place anything into it — the number of slots, what each slot means, and the direction. On circular sets, note explicitly whether entities face inward or outward, because "to the left of" reverses depending on the answer, and a set solved with the wrong orientation is solved correctly and answered wrongly.
Mixed structures are common and are not harder
A set may ask you to seat six people in a row and assign each a city and a profession. That is a linear frame with a matrix attached, not a new species of problem. Draw the line, then hang columns beneath it. Candidates who treat combined sets as exotic tend to abandon sets that were among the more tractable on the paper.
Ranking the conditions by strength
Before placing anything, number the conditions in the order you will apply them. This takes about twenty seconds and is the highest-return twenty seconds in the section.
| Rank | Type | Example | What it does |
|---|---|---|---|
| 1 | Fixing | "D sits in seat 3" | Removes all but one possibility for that entity |
| 2 | Blocking | "E and F sit together" | Turns two entities into one unit, shrinking the problem |
| 3 | Distance | "There are exactly two people between A and B" | Generates a small, enumerable set of placements |
| 4 | Relative | "G sits somewhere to the left of H" | Halves the space; useful for elimination, weak for placement |
| 5 | Negative | "C does not sit at either end" | Marks crosses; rarely places anyone directly |
| 6 | Conditional | "If J is in row 1, then K is in row 2" | Only fires once the antecedent is settled — apply last |
Conditional statements at rank six are frequently misapplied. "If J is in row 1, then K is in row 2" says nothing at all about K while J's position is unknown, and it says nothing about J if you discover K is not in row 2 — that direction requires the contrapositive, which is that J is not in row 1. Candidates lose sets by treating conditionals as though they run both ways.
A worked set
Six people — P, Q, R, S, T, U — sit in a row of six numbered seats, left to right. (i) S sits in seat 2. (ii) P and Q sit next to each other. (iii) There are exactly two seats between R and T. (iv) U does not sit at either end.
Rank first. (i) is fixing, (ii) is blocking, (iii) is distance, (iv) is negative — so the ranking says i, ii, iii, iv. One adjustment: a block is strong when the frame is tight and weak when it has many homes, and P–Q here can sit in several places. The distance condition yields only two. So the working order becomes i, iii, ii, iv.
Apply (i): S is in 2. Seats left for the other five: 1, 3, 4, 5, 6.
Apply (iii): exactly two seats between R and T means their positions differ by three. From the available seats that gives {1, 4} or {3, 6} — two cases, each with R and T in either order.
Test each against (ii). If R and T occupy 1 and 4, the free seats are 3, 5, 6 — and P, Q need adjacency, which 5 and 6 provide. U then takes 3, satisfying (iv). Consistent.
If R and T occupy 3 and 6, free seats are 1, 4, 5. P and Q must be adjacent, so 4 and 5, leaving U at seat 1 — which violates (iv). Eliminated. The first case is the arrangement, reached without enumerating all placements.
Note what did the work. Applying the distance condition before the blocking condition produced two cases instead of a dozen, and the negative condition — ranked last, and often the least useful for placing anyone — killed one of them outright. Started from P and Q's adjacency instead, this set generates many more branches for the same answer.
How long to your first placement?
Over three minutes before anything lands on the grid means the reading or the sequencing went wrong. The time view shows it.
- Time inside each set
- Sets completed vs started
- DILR percentile
Handling cases without drowning
Sometimes the conditions genuinely do not resolve to one arrangement and you must branch. Three rules keep that from consuming the set.
Two cases is normal. Four means you sequenced wrongly. If you find yourself with four or more live branches, stop and go back to the condition ranking rather than pushing forward. There is almost always a stronger condition you left unapplied, and applying it now costs thirty seconds against several minutes of parallel casework.
Draw cases side by side, never one after another. Two small frames next to each other let you kill one at a glance when the next condition is applied. Sequential working means rebuilding from scratch when a branch dies.
Test the weakest-looking condition against every case immediately. Negative and conditional statements are poor at placing entities and excellent at eliminating branches, which is exactly what you need once you are in casework. The condition you ranked last is often the one that ends the casework fastest.
The errors that waste most of the time
| Error | What it costs | Prevention |
|---|---|---|
| Building before reading everything | A structure that a later condition invalidates — six minutes lost | Read all conditions, then draw the frame |
| Holding negatives in your head | A forgotten cross produces a consistent-looking wrong arrangement | Mark every negative on the frame as a cross the moment you read it |
| Assuming an unstated adjacency | Solves a different problem correctly | "Next to" means adjacent; "near" and "on the same side" do not |
| Ignoring facing direction | Left and right invert; answers are wrong despite correct work | Write "facing centre" or "facing outward" on the frame before placing |
The second row deserves emphasis because it produces the worst outcome available: an arrangement that satisfies every condition you remembered, answers every question confidently, and is wrong. Errors that feel like errors cost you a set. Errors that feel like success cost you a set and four questions of misplaced confidence.
Key Takeaways
- Rank conditions before placing anything — fixing, blocking, distance, relative, negative, conditional.
- Draw the frame first, including slot count, meaning and facing direction.
- Mark negatives as crosses immediately. A remembered negative is a forgotten one.
- Four live cases means a sequencing error, not a hard set. Go back to the ranking.
- Conditionals run one way only. The reverse direction needs the contrapositive.
- Mixed structures are not harder — a line with columns hung beneath it is still a line.
People also search for
How do I solve arrangement questions in CAT DILR?
Read every condition before drawing anything, identify the structure, draw an empty frame, then rank the conditions by strength and apply them in that order rather than the order printed. Fixing conditions come first, then blocking, then distance, then relative, then negative, then conditional. This ordering typically turns a set that would generate a dozen branches into one that generates two, and the twenty seconds spent ranking is the highest-return time in the section.
Which condition should I apply first in a puzzle?
The one that fixes a position outright — "D sits in seat 3" — because it removes all but one possibility for that entity in a single move. Blocking conditions that tie two entities together come next, then distance conditions that generate a small enumerable set of placements. Relative conditions like "G is left of H" halve the space at best and are far better used for elimination later than for placement early.
What are the main types of arrangement sets in CAT?
Five structures cover almost all of them: linear arrangements in a row or ranking, circular arrangements around a table, matrix or grid sets matching entities against attributes, grouping sets that divide entities into teams with capacities, and sequencing sets ordered over time. Many real sets combine two — seating six people in a row while also assigning each a city and a profession is a linear frame with a matrix hung beneath it, not a separate species of problem.
How do I handle circular arrangement questions?
Fix one position as a reference point before placing anything else, since a circle has no inherent starting point and rotations of the same arrangement are identical. Then write the facing direction on the frame explicitly — inward or outward — because "to the left of" reverses depending on it. A set solved with the wrong orientation is solved correctly and answered wrongly, which is among the more painful ways to lose four questions.
What do I do when a puzzle produces multiple cases?
Two live cases is normal. Four or more usually means you sequenced the conditions wrongly, and the right response is to go back to the ranking rather than push forward — there is almost always a stronger condition left unapplied, and applying it costs thirty seconds against several minutes of parallel casework. Draw the cases side by side rather than one after another, so a single new condition can kill one at a glance.
How should I use negative conditions?
Mark them on the frame as crosses the moment you read them, never hold them in memory. A forgotten negative produces the worst outcome in the section: an arrangement that satisfies every condition you remembered, answers every question confidently, and is wrong. Negatives rarely place anyone directly, but they are excellent at killing branches once you are in casework — the condition you ranked last is often the one that ends the casework fastest.
Do conditional statements work in both directions?
No, and treating them as though they do loses sets. "If J is in row 1, then K is in row 2" tells you nothing about K while J's position is unknown. Discovering that K is not in row 2 does let you conclude something — that J is not in row 1 — but only through the contrapositive, which is a different statement from the converse. Apply conditionals last, once their antecedents are settled by other conditions.
How much time should an arrangement set take?
Eight to twelve minutes with a hard stop either way, depending on whether you are in practice or under the forty-minute sectional lock. A useful internal checkpoint is time to first placement: if nothing has landed on the frame after three minutes, either the reading was incomplete or the sequencing went wrong, and both are worth thirty seconds to fix rather than several minutes to work around.
Are combined arrangement sets harder?
Usually not, though they look it. A set that seats six people in a row and also assigns each a city and a profession is a linear frame with columns hung beneath it — the same frame, with more information attached to each slot. Extra attributes often supply extra constraints, which makes such sets more determined rather than less. Candidates who treat combined sets as exotic frequently abandon sets that were among the more tractable on the paper.
How do I practise arrangement questions effectively?
Whole sets, and record two things afterwards: which condition you applied first, and how long it took before anything landed on the frame. Sequencing errors are invisible unless written down, and most candidates discover they have been working conditions in printed order without ever noticing. When a set defeats you, re-attempt it with a different sequencing before reading any solution — a large share of failed sets are recoverable that way.