Puzzles: Reasoning Ability Notes for Manipur PSC

Reasoning Ability – Puzzles

For Manipur PSC – Comprehensive Study Notes

1. Simple Explanation

Puzzles in reasoning tests are problems that require you to arrange, order, or deduce relationships among a set of items (people, objects, events, etc.) based on a set of clues.

Goal: Identify the missing element or the correct sequence.
Common Formats:
- Seating/Line‑up puzzles
- Number sequence puzzles
- Logic grid puzzles
- Time‑based puzzles (e.g., schedules, travel time)
- Spatial puzzles (e.g., floor plans, block arrangements)

The key is to transform each clue into a logical statement and then systematically eliminate impossibilities.

2. Key Points & Strategies

#	Strategy	How to Use
1. Make a table	Create a grid/table to record all variables.	Columns = items, rows = positions/clues.
2. Write down every clue formally	Convert natural language into logical statements.	e.g., “A sits to the left of B” → `pos(A) < pos(B)`
3. Use elimination	Cross‑out impossible combinations.	If `C` cannot be at position 2, mark an “X” there.
4. Assign fixed positions early	If a clue fixes an item in a spot, put it down first.	“G is at the 3rd position” → place G.
5. Use “contrapositive” reasoning	If `pos(X) = 1` then `X` cannot be elsewhere.	Helps narrow down options.
6. Check for contradictions	After filling a few, test for any rule violation.	Back‑track if a rule is broken.
7. Keep track of “must‑be” vs “could‑be”	Some items are forced, others have options.	Focus on forced items first.
8. Use “distance” clues	“X is two places away from Y” → `	pos(X)-pos(Y)
9. Count remaining possibilities	If only one possibility remains, place it.	Avoids guessing.
10. Double‑check all clues	After completing, re‑read each clue to confirm compliance.	Avoids overlooked mistakes.

3. Worked Example

Problem

A group of six people – A, B, C, D, E, F – are seated in a row from left to right.
The following clues are given:

A sits somewhere to the left of C.
D sits immediately to the right of B.
E sits at one of the end seats.
C sits immediately to the left of E.
F sits somewhere to the right of D.

Question: What is the correct seating arrangement from left to right?

Step‑by‑Step Solution

Step	Action	Reason
1	Place E at an end seat (clue 3).	“E sits at an end”
2	From clue 4, C is immediately left of E.	So C must be next to E on the left.
3	Place E at the far right (position 6).	This satisfies “E at an end” and leaves space for C.
4	Place C at position 5.	Immediately left of E.
5	From clue 1, A is left of C.	So A can be at positions 1–4.
6	From clue 2, D sits immediately right of B.	So B and D are adjacent with D to the right.
7	From clue 5, F is right of D.	So F must be to the right of D but can’t occupy position 6 (E is there).
8	Since F is right of D and E is at position 6, D cannot be at position 5 (would force F at 6).	Eliminate that possibility.
9	Test D at position 4 → B at position 3.	Check: F must be right of D → F at position 5? No, 5 occupied by C.
10	Test D at position 2 → B at position 1.	Check F right of D → F can be at position 3 or 4. Both are free.
11	Place F at position 4 (any free spot satisfies all).	No contradictions.
12	Remaining person A must be at position 3.	It is the only free seat left and satisfies “A left of C (pos 5).”

Final seating (left → right):

B | 2. D | 3. A | 4. F | 5. C | 6. E

Verification:

A left of C → 3 < 5 ✔️
D immediately right of B → 2 = 1+1 ✔️
E at end → rightmost ✔️
C immediately left of E → 5 = 6-1 ✔️
F right of D → 4 > 2 ✔️

All clues satisfied.

4. Quick Revision Summary

Concept	Take‑away
Clues → Logic	Convert every sentence into a strict statement (e.g., “to the left of” = `<`, “immediately right” = `+1`).
Tables are your friend	A grid of items vs. positions keeps track of possibilities.
Fix the ends first	End seats or fixed positions usually narrow the search dramatically.
Distance matters	“Two places away” → absolute difference of 2.
Eliminate systematically	Mark