Once seating is understood, the rest of the analytical puzzles are the same idea wearing different clothes: assign each item to exactly one slot, subject to constraints. Orders of merit, meeting schedules, subject-and-city grids and team memberships are all one procedure.
The procedure is worth an afternoon because it is reusable: the same grid answers "who came first", "which day is free" and "who teaches what". Candidates who lack it treat each new puzzle as a fresh problem and run out of time by question 60.
Build a grid whose rows are the items and whose columns are the attributes, then let every condition cross out cells.
Three mechanics turn conditions into crosses:
When the grid stalls with two items and two attributes, add the one condition you have not used. Puzzles are designed with exactly enough conditions; the unused one always breaks the tie.
Four friends — A, B, C and D — each chose a different subject (Maths, Physics, Chemistry, Biology) and each comes from a different city (Lahore, Karachi, Quetta, Multan).
Filling the grid:
| Person | Subject | City |
|---|---|---|
| A | Maths | Multan |
| B | Biology | Karachi |
| C | Chemistry | Lahore |
| D | Physics | Quetta |
Note how the answer came from the fifth condition. Without "the Quetta person chose Physics", B and D would still be interchangeable — which is exactly the situation where a question can only ask "must be true".
Five meetings — M1, M2, M3, M4, M5 — are held on five consecutive weekdays.
Monday and Wednesday are taken, leaving Tuesday, Thursday and Friday. The pair [M4, M5] must be consecutive: the only free consecutive pair is Thursday and Friday. So M4 is on Thursday and M5 on Friday, which leaves M3 on Tuesday — consistent with the rule that it is not on Friday, which was the condition that stopped you from placing M3 last.
| Question shape | Method |
|---|---|
| Fully determined | There is one arrangement; read the answer off the grid |
| "Must be true" | Find what holds in every surviving case; test by trying to break it |
| "Could be true" | Test each option; reject any that breaks a condition |
| "Cannot be true" | Often fastest: look for the option that violates a given condition |
Six students are divided into two project teams of three. A and B must be on the same team. C must not be on a team with A. D must be with B.
Start from the strongest link: A, B and D must all be together, and that is already three people — the maximum team size — so team one is exactly {A, B, D}. C is not with A, so C is on team two with the remaining students E and F. The split is fully determined without any case work, purely because the team size acted as a constraint.
Counting before drawing is the habit worth taking from this example: limits on group size are among the most powerful conditions in the section, and they are the easiest to overlook because they are expressed as a fact about the setup rather than as a rule about a person.
In the scheduling puzzle, which meeting is on Tuesday?
In the person-subject-city grid, who is from Quetta?
Which subject did B choose?
Your grid still leaves two possible arrangements and the next question says "must be true". What do you do?
Without looking back: what are the three kinds of condition, and why do group-size limits matter so much?
The answer: definite conditions, relational conditions and negative conditions; group-size limits restrict everyone at once, because filling a group to its capacity removes the remaining people from it.
A condition such as "A teaches Maths" is a condition, while "the person from Lahore teaches Chemistry" is . The grid's rows are items and its columns are . Questions that ask what be true are answered by elimination.
Four teachers W, X, Y and Z teach four subjects (English, Urdu, Maths, Science) in four periods (1, 2, 3, 4). The Maths teacher takes period 2. Y teaches Urdu in period 4. W is not the Science teacher. Z takes period 1 and does not teach English. Work out the full timetable, then say which single extra condition would make the puzzle solvable in fewer steps.
Fill the definite facts: Y = Urdu, period 4; Z = period 1; Maths = period 2 (so Z, in period 1, is not Maths, and Y, in period 4, is not Maths).
Remaining periods for W and X are 2 and 3, and Maths must be in period 2, so whichever of W or X holds period 2 teaches Maths. Z does not teach English and does not teach Maths (period 1 is not period 2), so Z teaches either Science or Urdu — but Urdu belongs to Y, so Z teaches Science. Then W is not Science, and English, Maths and Urdu remain for W, X and Y; since Y has Urdu and period 4 is not Maths, the Maths teacher must be W or X in period 2.
Two cases survive: W = Maths in period 2 with X = English in period 3, or X = Maths in period 2 with W = English in period 3. One extra definite condition — "X teaches English" or "W takes period 2" — collapses it to a single timetable. It is a good habit to note, at the end of a puzzle, exactly which extra fact would finish it: that is what "must be true" questions are testing you for.
Ordering fixes each item to a slot. The next lesson removes the slots and keeps only the rules: grouping and selection puzzles, where items are sorted into teams and the leftover is a “not selected” set.