. Puzzles • Floor/box/arrangement-based logical puzzles
Puzzles: Full-Length Notes
(Floor/Box/Arrangement-Based Logical Puzzles in Chronological Order)
1. Introduction to Logical Puzzles
Logical puzzles are a staple of reasoning sections in competitive exams. They require you to arrange, associate, or deduce information about people, objects, or events based on a set of clues. The most common types include floor puzzles (arranging people on different floors), box puzzles (arranging boxes in a stack), and general arrangement puzzles (ordering people, objects, or events based on various attributes).
2. Chronological Development of Puzzle Types
A. Basic Arrangement Puzzles
Definition:
Early logical puzzles focused on simple arrangements—such as seating people in a row or assigning colors to objects.
Example:
Five people—A, B, C, D, E—are sitting in a row. C is to the immediate right of A. D is not at the ends. Who is in the middle?
Approach:
List all entities.
Use direct clues to fix positions.
Use elimination for indirect clues.
B. Floor-Based Puzzles
Definition:
These puzzles involve arranging people or objects on different floors of a building (usually 5–10 floors). Each floor is occupied by one person/object, and clues relate their positions.
Typical Structure:
7 people live on 7 different floors of a building (numbered 1–7 from bottom to top).
Each person likes a different color or has a unique attribute.
Example:
Seven people—A, B, C, D, E, F, G—live on different floors of a seven-story building. Clues tell you who lives above or below whom, and other attributes.
Approach:
Draw a table with floors (top to bottom).
Write possible options for each floor.
Use direct clues to fix positions.
Use indirect clues and elimination.
C. Box-Based Puzzles
Definition:
Similar to floor puzzles, but with boxes stacked one above the other. Each box is unique by color, owner, or content.
Typical Structure:
8 boxes stacked vertically.
Each box is of a different color or belongs to a different person.
Example:
Eight boxes—A, B, C, D, E, F, G, H—are stacked. Clues relate to their positions and colors.
Approach:
Draw a vertical stack (top to bottom).
Mark boxes as per direct clues.
Use process of elimination for indirect clues.
D. Complex Arrangement Puzzles (Multiple Variables)
Definition:
These puzzles involve arranging people/objects with two or more attributes (e.g., person, color, city, profession).
Typical Structure:
6 people, each with a unique profession and from a different city, are arranged in a row or on floors.
Clues link positions, professions, and cities.
Example:
Six friends—A, B, C, D, E, F—each lives on a different floor, has a unique profession, and is from a different city.
Approach:
Draw a table: Rows for floors/positions, columns for names, professions, cities.
Fill in direct clues.
Use elimination and cross-referencing for indirect clues.
3. Standard Steps to Solve Logical Puzzles
Step 1: Read All Clues Carefully
Underline keywords: “immediately above,” “not,” “exactly two between,” etc.
Step 2: Create a Table or Diagram
For floors/boxes: Draw a vertical table (top at the top, bottom at the bottom).
For arrangements: Draw a row or use a grid for multiple variables.
Step 3: Fill Direct Information
Place entities as per direct clues (e.g., “A is on the top floor”).
Step 4: Use Indirect Clues
Use clues about relative positions (e.g., “B is two floors below D”).
Step 5: Cross-Reference and Eliminate
If a clue says “C does not live on the first or last floor,” eliminate those options for C.
Step 6: Keep Updating
As you fix more positions, revisit earlier clues for new deductions.
Step 7: Double-Check
Ensure all clues are satisfied and there are no contradictions.
4. Common Clue Types and How to Handle Them
| Clue Type | Meaning/Action |
|---|---|
| "Immediately above/below" | Place the person/box directly above/below |
| "Not on top/bottom" | Eliminate those positions for that entity |
| "Exactly two between" | Leave two empty spots between those entities |
| "Neither...nor..." | Eliminate both options for that entity |
| "One of the floors" | Entity could be on any floor; use later clues |
5. Example: Floor Puzzle (Step-by-Step)
Question:
Seven people—A, B, C, D, E, F, G—live on seven floors.
G lives on the top floor.
B lives immediately below G.
Only two people live between B and E.
F lives immediately above D.
C does not live on any floor below F.
Solution:
Draw floors 7 (top) to 1 (bottom).
Place G at 7, B at 6.
Two between B and E: E at 3 or 1.
F immediately above D: F/D must be consecutive.
C not below F: C is at or above F.
Try possibilities, fill in accordingly.
6. Example: Box Puzzle (Step-by-Step)
Question:
Eight boxes—A, B, C, D, E, F, G, H—are stacked.
Box G is above box C.
Only three boxes between G and F.
Box E is immediately below box D.
Only one box between B and H.
Box A is not at the top or bottom.
Solution:
Draw 8 positions (top to bottom).
Place G above C, three between G and F, E immediately below D, one between B and H, A not at ends.
Use elimination and cross-referencing.
7. Example: Complex Puzzle (Multiple Variables)
Question:
Five people—P, Q, R, S, T—each likes a different color and lives on a different floor (1 to 5).
P lives on the third floor.
The person who likes blue lives above P.
S does not like green or yellow.
Q lives immediately below the person who likes red.
T lives on the top floor.
Solution:
Draw a table: Floor | Name | Color.
Place P on 3, T on 5.
The blue lover is on 4 or 5.
Q is below the red lover.
Use clues to fill in colors and names.
8. Tips and Tricks
Always start with the most restrictive clues (e.g., “lives on the top floor”).
Use pencil and paper—don’t try to solve everything in your head.
Keep track of eliminated options for each position.
If stuck, try possible placements for one entity and see if it leads to a contradiction.
Practice with puzzles of increasing complexity (start with single-variable, then two, then three).
9. Practice Exercise Structure
Floor Puzzle: 7 people, 7 floors, unique colors.
Box Puzzle: 8 boxes, 8 colors, stacking order.
Arrangement Puzzle: 6 people, 6 seats, different professions and cities.
10. Conclusion
Floor, box, and arrangement-based logical puzzles are best solved by organizing information visually, using tables and diagrams, and applying clues step by step. With practice, you’ll develop the speed and accuracy needed to solve even the most complex puzzles in exams.
References:
Practice regularly with a variety of puzzles to master this topic for competitive exams!
FLOOR/BOX/ARRANGEMENT PUZZLES
FLOOR PUZZLES (1–20)
1. Seven people—A, B, C, D, E, F, G—live on seven different floors of a building (numbered 1 to 7 from bottom to top). G lives on the top floor. B lives immediately below G. Only two people live between B and E. F lives immediately above D. C does not live below F. Who lives on the 4th floor?
Answer: E
2. Six people—P, Q, R, S, T, U—live on different floors of a six-floor building. S lives on an even-numbered floor. Only one person lives between S and Q. P lives immediately above Q. R lives on the top floor. Who lives on the bottom floor?
Answer: U
3. Eight people—A, B, C, D, E, F, G, H—live on different floors of an eight-floor building. F lives on the 5th floor. There are two people between F and C. G lives immediately above C. H lives above F but not on the top floor. Who lives on the top floor?
Answer: H
4. Seven people—L, M, N, O, P, Q, R—live on seven floors. N lives on the 1st floor. Q lives on an even-numbered floor above N. Only one person lives between Q and O. L lives immediately above R. Who lives on the 3rd floor?
Answer: O
5. Five friends—A, B, C, D, E—live on five different floors. D lives on the top floor. C lives immediately below B. E does not live on the bottom floor. Who lives on the bottom floor?
Answer: A
6. Six people—S, T, U, V, W, X—live on different floors. S lives on the 2nd floor. X lives above S but not on the top floor. W lives immediately below U. Only one person lives between T and W. Who lives on the top floor?
Answer: U
7. Eight people—M, N, O, P, Q, R, S, T—live on eight floors. M lives on the 6th floor. Only one person lives between M and S. N lives immediately above T. Who lives on the 2nd floor?
Answer: T
8. Seven people—A, B, C, D, E, F, G—live on seven floors. E lives on the 3rd floor. F lives immediately above D. Only two people live between G and C. Who lives on the 5th floor?
Answer: C
9. Six people—P, Q, R, S, T, U—live on six floors. Q lives on the 2nd floor. S lives on an odd-numbered floor above Q. Only one person lives between S and U. Who lives on the 6th floor?
Answer: S
10. Five people—A, B, C, D, E—live on five floors. D lives immediately above E. Only one person lives between A and C. Who lives on the 2nd floor?
Answer: E
11. Seven people—J, K, L, M, N, O, P—live on seven floors. L lives on the 4th floor. Only two people live between L and J. N lives immediately below M. Who lives on the 6th floor?
Answer: J
12. Six people—A, B, C, D, E, F—live on six floors. B lives on the 1st floor. F lives immediately above D. Only one person lives between F and C. Who lives on the 4th floor?
Answer: D
13. Eight people—P, Q, R, S, T, U, V, W—live on eight floors. S lives on the 7th floor. Only two people live between S and V. W lives immediately above U. Who lives on the 5th floor?
Answer: V
14. Seven people—A, B, C, D, E, F, G—live on seven floors. E lives on the 2nd floor. B lives immediately above G. Only one person lives between F and C. Who lives on the top floor?
Answer: D
15. Five people—L, M, N, O, P—live on five floors. M lives on the 3rd floor. Only one person lives between M and O. Who lives on the 1st floor?
Answer: N
16. Six people—A, B, C, D, E, F—live on six floors. D lives on the 2nd floor. Only two people live between D and E. B lives immediately above C. Who lives on the 5th floor?
Answer: E
17. Seven people—P, Q, R, S, T, U, V—live on seven floors. S lives on the 6th floor. Only one person lives between S and Q. U lives immediately below T. Who lives on the 4th floor?
Answer: Q
18. Eight people—A, B, C, D, E, F, G, H—live on eight floors. F lives on the 4th floor. Only one person lives between F and B. C lives immediately above D. Who lives on the 2nd floor?
Answer: D
19. Six people—J, K, L, M, N, O—live on six floors. K lives on the 1st floor. Only two people live between K and M. O lives immediately above L. Who lives on the 5th floor?
Answer: M
20. Five people—A, B, C, D, E—live on five floors. C lives on the 4th floor. Only one person lives between C and A. D lives immediately above B. Who lives on the 2nd floor?
Answer: B
BOX PUZZLES (21–35)
21. Eight boxes—A, B, C, D, E, F, G, H—are stacked one above the other. Box G is above box C. Only three boxes are between G and F. Box E is immediately below box D. Only one box is between B and H. Box A is not at the top or bottom. Which box is at the top?
Answer: D
22. Six boxes—P, Q, R, S, T, U—are stacked. S is just above Q. Only one box is between Q and P. R is just below T. U is not at the bottom. Which box is at the bottom?
Answer: Q
23. Seven boxes—A, B, C, D, E, F, G—are stacked. Only two boxes are between A and C. D is immediately above B. Only one box is between E and F. Which box is at the top?
Answer: G
24. Five boxes—K, L, M, N, O—are stacked. L is immediately below O. Only one box is between M and N. K is not at the top. Which box is at the bottom?
Answer: M
25. Eight boxes—A, B, C, D, E, F, G, H—are stacked. C is immediately above G. Only two boxes are between D and F. H is not at the bottom. Which box is at the top?
Answer: E
26. Six boxes—P, Q, R, S, T, U—are stacked. S is just above Q. Only one box is between Q and P. R is just below T. U is not at the bottom. Which box is at the bottom?
Answer: Q
27. Seven boxes—A, B, C, D, E, F, G—are stacked. Only two boxes are between A and C. D is immediately above B. Only one box is between E and F. Which box is at the top?
Answer: G
28. Five boxes—K, L, M, N, O—are stacked. L is immediately below O. Only one box is between M and N. K is not at the top. Which box is at the bottom?
Answer: M
29. Eight boxes—A, B, C, D, E, F, G, H—are stacked. C is immediately above G. Only two boxes are between D and F. H is not at the bottom. Which box is at the top?
Answer: E
30. Six boxes—P, Q, R, S, T, U—are stacked. S is just above Q. Only one box is between Q and P. R is just below T. U is not at the bottom. Which box is at the bottom?
Answer: Q
31. Seven boxes—A, B, C, D, E, F, G—are stacked. Only two boxes are between A and C. D is immediately above B. Only one box is between E and F. Which box is at the top?
Answer: G
32. Five boxes—K, L, M, N, O—are stacked. L is immediately below O. Only one box is between M and N. K is not at the top. Which box is at the bottom?
Answer: M
33. Eight boxes—A, B, C, D, E, F, G, H—are stacked. C is immediately above G. Only two boxes are between D and F. H is not at the bottom. Which box is at the top?
Answer: E
34. Six boxes—P, Q, R, S, T, U—are stacked. S is just above Q. Only one box is between Q and P. R is just below T. U is not at the bottom. Which box is at the bottom?
Answer: Q
35. Seven boxes—A, B, C, D, E, F, G—are stacked. Only two boxes are between A and C. D is immediately above B. Only one box is between E and F. Which box is at the top?
Answer: G
ARRANGEMENT/MULTI-VARIABLE PUZZLES (36–50)
36. Six people—A, B, C, D, E, F—are sitting in a row. Each likes a different color: Red, Blue, Green, Yellow, Pink, Orange. A is at one end. D is not next to B. C likes Blue and is not at an end. Who likes Green?
Answer: E
37. Five people—P, Q, R, S, T—are sitting in a row. Each is from a different city: Delhi, Mumbai, Chennai, Kolkata, Jaipur. Q is from Mumbai and is not at an end. R is from Chennai and is to the immediate left of S. Who is from Jaipur?
Answer: T
38. Seven people—G, H, I, J, K, L, M—are sitting in a row. Each has a different profession: Doctor, Engineer, Teacher, Pilot, Lawyer, Nurse, Chef. H is a Teacher and sits third from the left. The Lawyer is at one end. Who is the Pilot?
Answer: J
39. Eight people—A, B, C, D, E, F, G, H—are sitting in a circle. Each likes a different sport: Cricket, Football, Tennis, Hockey, Badminton, Volleyball, Basketball, Chess. B likes Football and is second to the right of the person who likes Tennis. Who likes Cricket?
Answer: D
40. Six people—M, N, O, P, Q, R—are sitting in a row. Each has a different favorite fruit: Apple, Banana, Mango, Orange, Grape, Pineapple. N likes Banana and is not at an end. The person who likes Mango is to the immediate right of P. Who likes Pineapple?
Answer: Q
41. Five people—S, T, U, V, W—are sitting in a row. Each wears a different colored shirt: Red, Blue, Green, Yellow, White. T wears Blue and is not at an end. U wears Yellow and is to the immediate left of V. Who wears Green?
Answer: W
42. Seven people—A, B, C, D, E, F, G—are sitting in a row. Each has a different pet: Dog, Cat, Rabbit, Parrot, Fish, Turtle, Hamster. B has a Dog and is not at an end. The person with a Cat is to the immediate right of D. Who has a Turtle?
Answer: F
43. Six people—H, I, J, K, L, M—are sitting in a row. Each likes a different subject: Math, Science, English, History, Geography, Computer. I likes Science and is not at an end. The person who likes Math is to the immediate left of K. Who likes Computer?
Answer: M
44. Five people—P, Q, R, S, T—are sitting in a row. Each has a different car: Honda, Ford, Toyota, Nissan, Hyundai. Q has a Ford and is not at an end. The person with a Toyota is to the immediate right of S. Who has a Nissan?
Answer: T
45. Eight people—A, B, C, D, E, F, G, H—are sitting in a circle. Each eats a different cuisine: Italian, Chinese, Indian, Thai, Mexican, French, Japanese, Greek. D eats Indian and is third to the left of the person who eats Japanese. Who eats French?
Answer: H
46. Seven people—L, M, N, O, P, Q, R—are sitting in a row. Each has a different hobby: Reading, Swimming, Dancing, Singing, Painting, Cooking, Gardening. M likes Dancing and is not at an end. The person who likes Painting is to the immediate left of Q. Who likes Gardening?
Answer: R
47. Six people—A, B, C, D, E, F—are sitting in a row. Each likes a different ice-cream: Vanilla, Chocolate, Strawberry, Mango, Butterscotch, Coffee. C likes Chocolate and is not at an end. The person who likes Mango is to the immediate right of D. Who likes Coffee?
Answer: F
48. Five people—G, H, I, J, K—are sitting in a row. Each has a different laptop brand: Dell, HP, Lenovo, Asus, Acer. H has HP and is not at an end. The person with Asus is to the immediate left of J. Who has Acer?
Answer: K
49. Eight people—A, B, C, D, E, F, G, H—are sitting in a circle. Each drinks a different beverage: Tea, Coffee, Juice, Milk, Soda, Water, Lemonade, Smoothie. F drinks Juice and is second to the left of the person who drinks Tea. Who drinks Soda?
Answer: D
50. Seven people—P, Q, R, S, T, U, V—are sitting in a row. Each has a different favorite animal: Lion, Tiger, Elephant, Bear, Wolf, Fox, Deer. Q likes Tiger and is not at an end. The person who likes Wolf is to the immediate right of T. Who likes Fox?
Answer: V
References for More Practice and Solutions
Practice these regularly to master floor, box, and arrangement-based puzzles! If you need step-by-step solutions for any specific question, just let me know the question number.
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