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Puzzles & Syllogism

In the DSSSB AE Civil syllabus under General Intelligence & Reasoning · 2 parts

Puzzles · Syllogism

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📑 Contents (14 sections)

Part 1 of 2

Puzzles

Last reviewed 22 Sept 2026 · 6 min read

Every matching puzzle is a grid

Five people, five cities, five subjects — that is two grids, or one table with three columns. Draw the table before reading the clues a second time.

Rows: the fixed set that never changes — usually the people, or the floors 1 to 7.
Columns: each attribute to be matched.
Fill a cell only when a clue forces it; write a small ✗ in a cell a clue forbids.
Re-read the clue list from the top every time a new cell is filled: clues that were useless often become decisive.

Exam TipThe order that saves time

Definite clues ("C lives on floor 3") → relative clues ("A lives two floors above B") → negative clues ("D does not teach physics"). A negative clue is worth little at the start and a great deal at the end.

Floor and stack puzzles

Seven floors, seven people: number the floors with 1 at the bottom and say so on your paper. Then:

"A lives above B" means A's number is larger.
"Exactly two people live between A and B" means their numbers differ by 3.
"A lives immediately above B" means $A = B + 1$ .
The topmost and bottommost floors are the most constrained — clues about them are usually the ones to use first.

The same layout handles boxes stacked one on another and books piled on a shelf.

Scheduling puzzles

Days of the week, months, or dates in a month. Write the days in order along the top and mark what is fixed. Watch for two traps: a week that runs Monday to Sunday versus Sunday to Saturday, and clues that talk about "the day before" a day that is itself unknown.

Carrying two cases

When a clue allows two placements, start Case 1 and Case 2 side by side. Continue both until a later clue contradicts one. Deciding early which case "feels right" is the commonest reason a puzzle takes twenty minutes instead of four.

A worked puzzle

Five friends — Amit, Bina, Chetan, Deepa and Esha — live on five floors of a building (1 at the bottom to 5 at the top). Each likes a different colour: red, blue, green, white, yellow.

Chetan lives on floor 4.
The one who likes red lives immediately below Chetan.
Amit lives on the topmost floor.
Bina does not live on floor 1.
The one who likes blue lives on floor 1.
Deepa likes green.
Esha does not like white.

Worked ExampleSolving it clue by clue

From 1 and 3: Chetan is on 4, Amit on 5. Floors 1, 2 and 3 are left for Bina, Deepa and Esha; by 4, Bina is on 2 or 3.

From 2: the red-lover is on floor 3. From 5: the blue-lover is on floor 1. From 6: Deepa likes green, so Deepa is not on floor 1 or 3 → Deepa is on floor 2, so Bina is on 3 and Esha on 1.

So Bina (floor 3) likes red and Esha (floor 1) likes blue. By 7 Esha does not like white, which is consistent. White and yellow are left for Amit and Chetan, and no clue separates them — the puzzle fixes the floors and three colours, and leaves white and yellow undetermined.

Floor	Person	Colour
5	Amit	white or yellow
4	Chetan	white or yellow
3	Bina	red
2	Deepa	green
1	Esha	blue

A real exam set would add an eighth clue, such as "Chetan does not like yellow", which finishes the grid at once. Noticing what is not determined is itself a skill: several questions ask exactly that.

Worked examples

Worked ExampleExample 1 — floors and a gap

In a seven-floor building, P lives on floor 2 and exactly three people live between P and Q. Where does Q live?

Solution. Their floor numbers differ by 4 → Q is on floor 6 (floor $- 2$ does not exist).

Worked ExampleExample 2 — immediately above

R lives immediately above S, and S lives on floor 3 of six. Who lives on floor 4?

Solution. R.

Worked ExampleExample 3 — a negative clue at the right time

Four people A, B, C, D take four subjects: maths, physics, chemistry, biology. A does not take maths or physics. B takes chemistry. C does not take biology. What does A take?

Solution. A takes chemistry or biology; chemistry is B's, so A takes biology. Then C takes maths or physics, and D takes the other.

Worked ExampleExample 4 — days

A meeting is on a day between Tuesday and Friday, but not on Wednesday. Which day is it?

Solution. Between Tuesday and Friday means Wednesday or Thursday; not Wednesday → Thursday.

Worked ExampleExample 5 — two cases

In a row of five boxes, box P is somewhere above box Q, and exactly one box lies between them. Box Q is not at the bottom. List the possible positions of P and Q.

Solution. Q at 2 → P at 4; Q at 3 → P at 5. Two cases survive, and neither can be ruled out without another clue.

Frequently tested points

Draw the grid first; fill only what a clue forces, and mark ✗ for what it forbids.
Use definite clues, then relative, then negative.
In floor puzzles, state which end is floor 1 on your own paper.
"Exactly $k$ between" means the numbers differ by $k + 1$ .
Carry two cases side by side rather than guessing.
Re-read the clue list after every new entry.

Common MistakeCommon mistakes

Filling a cell on a hunch and building the rest of the grid on it.
Reading "above" as a bigger number in one puzzle and a smaller one in the next — fix the convention once.
Treating "between A and B" as an order.
Abandoning a case too early, or forgetting to finish the second one.
Missing that the puzzle genuinely leaves something open.

Revision SummaryChapter summary

Matching puzzles are grids: rows for the fixed set, columns for each attribute.
Clues are used in order — definite, relative, then negative.
Floor and box puzzles need an explicit numbering convention before anything else.
When a clue allows two placements, both are carried until one is contradicted.
Recognising what the clues do not determine is part of the answer, not a failure.

Part 2 of 2

Syllogism

Last reviewed 22 Sept 2026 · 5 min read

The four forms

Form	Statement	What it allows
A (universal affirmative)	All A are B	every A is inside B; B may be bigger
E (universal negative)	No A is B	the circles do not touch
I (particular affirmative)	Some A are B	the circles overlap; they may also coincide
O (particular negative)	Some A are not B	part of A lies outside B

RememberThe one rule

A conclusion is valid only if it holds in every diagram the statements allow. One legal diagram in which it fails is enough to reject it. So the work is not to draw a diagram, but to draw the diagram that commits to the least — and then to try to break the conclusion.

Drawing the least-committed diagram

All A are B: A wholly inside B. (Do not make them equal unless forced.)
No A is B: two separate circles.
Some A are B: two overlapping circles — and remember that "some" does not deny "all".
Some A are not B: A overlapping B with a part of A clearly outside.

Then read the conclusion and ask: can I redraw this, still obeying the statements, so that the conclusion becomes false? If yes, it does not follow.

Conversions that are always safe

All A are B → Some B are A (and Some A are B).
No A is B → No B is A, and Some A are not B.
Some A are B → Some B are A.
Some A are not B → nothing about B and A in reverse.

Possibility conclusions

Modern papers ask about possibility: "All A being C is a possibility." Such a conclusion is true when at least one legal diagram contains it — the mirror image of the main rule. So:

A definite conclusion needs every diagram.
A possibility conclusion needs one diagram.

Either-or (complementary pairs)

When neither conclusion follows alone, but together they cover every case and overlap in none, the answer is either I or II follows. The pair must:

have the same subject and predicate, and
be of the forms (Some A are B, No A is B) or (All A are B, Some A are not B).

Worked examples

Worked ExampleExample 1 — the basic test

Statements: All pens are books. All books are tables. Conclusions: I. All pens are tables. II. Some tables are pens.

Solution. Pens inside books inside tables, in every legal drawing → I follows. From "all pens are tables", some tables are pens → II follows. Both follow.

Worked ExampleExample 2 — a middle term that does not connect

Statements: Some cats are dogs. Some dogs are rats. Conclusions: I. Some cats are rats. II. No cat is a rat.

Solution. Cats and rats may overlap, or may not — both drawings are legal, so neither conclusion follows on its own. But the two together cover every case and overlap in none → either I or II follows.

Worked ExampleExample 3 — a negative statement

Statements: All fruits are sweet. No sweet thing is bitter. Conclusions: I. No fruit is bitter. II. Some bitter things are fruits.

Solution. Fruits lie inside sweet, which is separate from bitter → I follows in every drawing; II contradicts it → only I follows.

Worked ExampleExample 4 — "some" does not mean "not all"

Statements: Some books are pens. All pens are red. Conclusions: I. Some books are red. II. All books are red.

Solution. The books that are pens are red → I follows. II fails in the drawing where other books lie outside red → only I follows.

Worked ExampleExample 5 — possibility

Statements: All roses are flowers. Some flowers are red. Conclusion: All roses being red is a possibility.

Solution. A legal drawing exists with every rose inside the red region → the possibility holds.

Worked ExampleExample 6 — a trap with "only"

Statement: Only boys can play. Conclusion: All who play are boys.

Solution. "Only A are B" means all B are A → the conclusion follows. Note it does not mean that all boys play.

Worked ExampleExample 7 — three statements

Statements: All A are B. No B is C. Some C are D. Conclusions: I. No A is C. II. Some D are not B.

Solution. A inside B, and B separate from C → I follows. The C's that are D lie outside B, so some D are not B → II follows. Both follow.

Worked ExampleExample 8 — reverse syllogism

Which set of statements makes "Some pens are papers" definitely true? (a) All pens are books, all books are papers (b) Some pens are books, some books are papers

Solution. (a) — pens inside books inside papers forces the overlap. In (b) the middle term connects nothing.

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