Allocation and Selection Sets in DILR: The Matrix Method

DILR

Twelve minutes into an allocation set, your page holds a web of arrows, three crossed out names, and one confident assignment you are no longer sure about. You started well. Somewhere around the fourth condition, the picture in your head and the picture on paper stopped matching.

Allocation and selection sets are some of the most solvable puzzles in DILR, and they are also where working memory breaks down fastest. The cure is a matrix: a single grid that holds every fact, so your head does not have to. This guide shows a five pass method for assigning people to tasks and for choosing teams under conditions.

Why Allocation Sets Eat Time and How a Grid Fixes It

DILR sets are not chapter based in the way Quant is, and the types and counts shift from year to year. What stays steady is that arrangements, selection, distribution and scheduling sets keep appearing in one form or another. Allocation, where you assign people to tasks, is a close cousin of all of them.

The reason these sets feel slow is that the conditions arrive as prose. "Asha does not take the audit." "Charu does the client call or the budget." Each sentence is easy alone. Together they require you to hold a dozen small facts at once, and the human mind handles that badly under a clock.

A grid moves the facts out of your head and onto the page. Rows hold the people, columns hold the tasks, and every cell holds one of three states: possible, ruled out, or confirmed. Once a fact is written into the grid you can forget it, because the grid remembers.

That is the real value of the matrix method. It is not faster at the arithmetic of the puzzle. It is faster because it frees working memory, a limit we explore in our piece on why DILR tests working memory and not just logic.

The Five Pass Matrix: One Routine for Every Assignment Set

The method has five passes. Each pass handles one kind of information, and doing them in order stops you from reasoning with half the facts missing.

Why this order? Because information arrives in layers. Hard facts are certain, so they go in first and shrink the grid for free. Singles are certain consequences of those facts, so they come next. Conditional rules are only sometimes active, so they wait on the side. Branching is the last resort because it multiplies your work. Reversing any of these steps makes the page messier without making the puzzle easier.

It also helps to decide the grid shape up front. For one to one assignments use a square grid. For many to one assignments, where several people may share a task, use the same grid but allow more than one tick in a column. For scheduling, where tasks sit in slots, add the slot as a third axis or use one grid per slot.

Pass three deserves a word. Conditional rules, such as "if Asha does design then Dev does not do budget", cannot be entered as a cross or a tick until you know the condition's trigger. Keep them in a short list beside the grid and check them each time the grid changes. They often turn into direct facts a few steps later.

Passes One to Four: A Worked Assignment

Here is a small set written for practice. Four people, Asha, Bhavin, Charu and Dev, take four tasks: audit, budget, client call and design. Asha does not do audit or budget. Bhavin does not do design. Charu does either the client call or the budget. Dev does not do the client call or the audit. Each person takes exactly one task.

Passes one and two give you the grid with crosses. Asha is left with client call and design. Bhavin has audit, budget and client call. Charu has client call and budget. Dev has budget and design. Now look at the audit column: Asha is out, Charu is out, Dev is out. Only Bhavin remains, so Bhavin does the audit. That is pass four, a forced single.

Ticking the audit for Bhavin crosses out his other cells. The grid now has three rows with two open cells each: Asha has client call and design, Charu has client call and budget, and Dev has budget and design. No row or column has a single open cell, so pass four stops. You have reached a cycle.

A cycle is not a failure. It means the stated conditions leave two consistent assignments, and the question must either supply one more fact or ask something that holds in both. That is where branching comes in.

Pass Five: Branching on a Cycle

In our example the cycle has two solutions. Either Asha takes client call, Charu takes budget and Dev takes design, or Asha takes design, Charu takes client call and Dev takes budget. Draw two small grids, one for each, and carry both.

Now suppose the next part of the set says Dev does not do design. That kills the first grid immediately, because Dev does design there. Only the second survives: Asha does design, Charu does the client call, and Dev does the budget. Check it against every original condition. Asha avoids audit and budget, Bhavin avoids design, Charu has the client call, and Dev avoids the client call and audit. All hold.

The lesson is that branching is cheap when the cycle is small. Two grids, carried side by side, let later conditions do the cutting. Resist the urge to guess one branch and continue, because a wrong guess found late costs far more than carrying both from the start.

If you find that a wrong early step has broken your page, our guide on how to recover from a wrong start on a DILR set shows how to rescue the grid or decide to leave the set. Some sets also yield answers without a full grid, as discussed in DILR questions solvable without a full arrangement.

It is worth checking every question against both grids even when only one survives later. Some questions ask what must be true in every valid assignment, and with two live grids you can read the answer directly: whatever is common to both is forced. In our example, Bhavin does the audit in both grids, so it holds in every valid assignment regardless of the extra condition.

Selection Sets: Use a Case Table Instead of a Grid

Selection sets ask you to choose a subset, such as a team of three from five people, under conditions. A grid of pairs does not suit them. A case table does, because you are tracking who is in and who is out across a handful of valid teams.

Take five people, P, Q, R, S and T, and a team of three. Conditions: P and Q are not both in, R is in only if S is in, and T is in only if Q is in.

Split on Q, the person with the most links. If Q is in, then P is out, and the team needs two more from R, S and T. The pair R and T fails because R needs S. The pairs R and S, and S and T, work.

If Q is out, T is out as well. The team must come from P, R and S, which works because R has S with it. If P is also out the team cannot reach three, so that case dies. The valid teams are Q, R, S; Q, S, T; and P, R, S. Notice that S is in every valid team, which is the kind of fact a question is likely to ask about.

Set type	Best tool	First move
Allocation, one to one	Grid of people and tasks	Enter hard facts and exclusions
Selection of a subset	Case table	Split on the person with most links
Allocation with a cycle	Two carried grids	Branch on the smallest ambiguity

A Practice Routine for Allocation and Selection Sets

Practise the five passes on small sets first, because speed on a four by four grid transfers to larger ones. Solve three or four sets a week, and write the pass number next to each major step. The labelling forces the order, which is what you will need under a clock.

After each set, record where you lost time. Common culprits are drawing the grid late, entering conditions in the wrong order, and branching too early. A short note on the cause tells you which pass to rehearse. If you struggle to decide which sets to attempt at all, read how to predict which DILR set is the sitter.

Real papers give the best test. Our topic wise CAT previous year questions include actual selection and arrangement style sets with solutions, so you can compare your grid with a worked one.

Sets that distribute items among groups use a similar grid. When you are comfortable with allocation, try CAT DILR distribution sets, where the rows and columns carry counts instead of ticks.