How to Solve Logical Reasoning Puzzles Step by Step

The short answer: do not solve a puzzle in your head. Draw a frame, enter the facts that are certain, branch only when you must and check your final arrangement against every condition. A clean diagram turns most puzzles into a sequence of small deductions.

Why puzzles go wrong

Most errors in puzzles come from three habits: holding facts in memory instead of on paper, committing to a guess without exploring the alternative and failing to re-check the full set of conditions at the end. The method below targets each.

The method in seven steps

1. Read the whole puzzle once before drawing anything, to see how many items and what kind of arrangement (line, circle, table).
2. Draw the frame: boxes in a row, a circle with positions or a table with rows and columns.
3. Enter definite facts first: statements like "A sits at the extreme left" or "B is on the third floor" go in immediately.
4. Combine conditions that share an item, to form chains: "C is to the left of D" and "D is to the left of E" give C, D, E in order.
5. Branch when forced: if a statement allows two placements, draw both cases side by side and carry both forward.
6. Eliminate cases that break a condition.
7. Verify the final arrangement against every statement before answering.

A worked seating example (original)

Six friends, A, B, C, D, E and F, sit in a row facing north, in seats 1 to 6 from left to right. Conditions:

1. A sits at one of the ends.
2. B sits second to the right of A.
3. C sits immediately to the left of D.
4. E does not sit next to B.

Question: who sits at seat 4?

Step 1: frame. Seats 1 to 6 in a row.

Step 2: branch on A. A is at seat 1 or seat 6. If A is at seat 6, then "second to the right of A" is impossible (no seats to the right), so A is at seat 1. Now B is second to the right of A: seat 3.

Step 3: place C and D. C is immediately left of D, so they occupy two adjacent seats with C on the left. Free seats are 2, 4, 5, 6. Adjacent free pairs: (4, 5) and (5, 6). Seat 2 is next to 1 and 3, both occupied, so it cannot hold a pair with seat 3 (B). So C, D = (4, 5) or (5, 6).

Step 4: place E. E is not next to B (seat 3), so E is not at seat 2 or seat 4.

• Case 1: C, D = (4, 5). Remaining seats: 2 and 6, for E and F. E cannot be at seat 2, so E is at seat 6 and F at seat 2. Check: E at 6 is not next to B at 3. Valid. Arrangement: A, F, B, C, D, E.
• Case 2: C, D = (5, 6). Remaining seats: 2 and 4, for E and F. E cannot be at seat 2 or 4, so there is no place for E. Invalid.

Only case 1 survives, so the arrangement is A, F, B, C, D, E, and seat 4 is C. Verify: A is at an end (yes); B is second to the right of A (seat 3, yes); C is immediately left of D (seats 4, 5, yes); E at seat 6 is not next to B at seat 3 (yes).

Notice what made it quick: the first branch (A at seat 6) died at once, and the second branch died at E. Without the diagram, it is easy to lose track.

Other puzzle types and how the method adapts

Habits that save time

• Write initials, not names.
• Use arrows for relative positions (A → B means A is left of B).
• Cross out impossible positions in a small table beside the frame.
• Skip the longest puzzle on the first pass and return if time permits. See how to pick which questions to skip.
• Answer all questions of a set once the arrangement is solved: they are quick after the setup.

How to practise

1. Start with small puzzles (4 or 5 items) untimed, using the seven steps.
2. Move to 6 to 8 items and set a time limit of about seven minutes.
3. After each puzzle, write down which step took the longest.
4. Redo wrong puzzles two days later.

Related practice: syllogisms, blood relations and direction sense. See also CAT DILR, banking reasoning and MAT Intelligence and Critical Reasoning for how puzzles appear in exams.

Common mistakes

• Solving mentally.
• Committing to one placement without checking the alternative.
• Forgetting to apply the last condition at the end.
• Misreading left and right, especially when people face each other.
• Spending ten minutes on one puzzle.