Multi-Layer Puzzles Worksheet 1 - Beginner Level (multi-dimensional puzzles) | 20 Questions

Question 1

Five runners are racing on three parallel tracks. Multiple runners can use the same track, and each runner's position is tracked within their track. Given information: • Alice and Diana are on Track 1 • Bob and Ethan are on Track 2 • Charlie is alone on Track 3 • On Track 1: Alice is ahead of Diana • On Track 2: Bob is ahead of Ethan • The person on Track 3 is running unopposed What is Diana's position within their track?

Step-by-step Solution:

Layer 1: Track Assignment (Horizontal Layer)
- Track 1: Alice, Diana
- Track 2: Bob, Ethan
- Track 3: Charlie

Layer 2: Position within Track (Competitive Layer)

Track 1 Rankings:
- Alice is ahead of Diana
- Therefore: Alice = 1st, Diana = 2nd

Track 2 Rankings:
- Bob is ahead of Ethan
- Therefore: Bob = 1st, Ethan = 2nd

Track 3 Rankings:
- Charlie = 1st (unopposed)

Cross-Track Analysis:
Diana is on Track 1 and is behind Alice.
Within Track 1, Diana is in 2nd position.

Answer: 2nd

horizontal-layering, parallel-tracks, comparative-position

Question 2

Five people live on five different floors of a building (numbered 1 to 5 from bottom to top). Each person likes a different color. Given information: • Amit lives on floor 3. • The person who likes White lives 3 floors away from Sneha. • Sneha does not like Yellow and is not on a floor adjacent to Rohan. • The person who likes Red lives immediately below Amit. Who lives on floor 4?

Step-by-step Solution (Requires Deduction Grid):

1. Establish Knowns and Direct Assignments:
- Clue 1: Amit is on Floor 3 (Floor 3).
- Clue 4: The person liking Red (Color X) is on the floor immediately below Amit. Since Amit is on Floor 3, the person liking Color X must be on Floor 2.
- This means the person on Floor 3 is Amit, and the person on Floor 2 is the one liking Red.

2. Resolve Relative Positional Clues (Clue 2):
- Sneha is on Floor 1.
- The person liking White is on Floor 4 (3 floors away from Sneha). This helps place the color White on Floor 4.

3. Apply Exclusionary Clue (Clue 3):
- Sneha is on Floor 1. We know their color is NOT Yellow (the color on Floor 5). This helps narrow down the color possibilities for Floor 1.
- We also know Sneha is NOT adjacent to the target person on Floor 4, which is true as they are on F1.

4. Final Arrangement (Deduction):
By combining the fixed positions (F3 and F2) with the positional link (Clue 2) and the exclusions, the only unique arrangement is:

| Floor | Person | Color |
| :---: | :---: | :---: |
| 5 | Priya | Yellow |
| 4 | Rohan | White |
| 3 | Amit | Blue |
| 2 | Vikram | Red |
| 1 | Sneha | Green |

Answer: Rohan

vertical-layering, floor-puzzle, deductive-2-layer

Question 3

Five boxes (A, B, C, D, E) are stacked vertically (Position 1 is bottom, 5 is top). Each box is painted a different color from: Green, Blue, Red, Yellow, White. Given information: • Box A is at the bottom (Position 1). • The White box is at the top (Position 5). • Box C is immediately above Box B. • The box at Position 3 is Red. • Box D is not Green. What color is Box C?

Step-by-step Solution:

1. Direct Placements:
- Position 1: Box A (Green)
- Position 5: Box E (White)
- Position 3: Red

2. Build Complete Stack:

| Position | Box | Color |
|----------|-----|-------|
| 5 | E | White |
| 4 | D | Yellow |
| 3 | C | Red |
| 2 | B | Blue |
| 1 | A | Green |

3. Find Box C:
- Box C is at Position 3
- Its color is Red

Answer: Red

vertical-layering, stacking, deductive-color-coding

Question 4

Five individuals must be matched to their Car, Pet, and City of residence. No two individuals share any of these attributes. Given information: • **Either** the person with the **Fish** lives in **Boston**, **OR** the person with the **Bird** drives a **Van**. • The person in **NY** does not own a **Cat** and does not drive a **SUV**. • If a person drives a **Truck**, their city is not **Miami**. • **Carl** is the one who owns the **Cat**. • The person who drives a **Hatchback** is **Evan**, who is also the one from **LA**. If you assume the second part of the Bi-Conditional clue (Clue 1) is **true**, what car does Alex drive?

Step-by-step Solution (Requires Case-Based Reasoning):

1. Analyze the Bi-Conditional Clue (Clue 1):
- Clue 1: (Pet=Fish → City=Boston) OR (Pet=Bird → Car=Van)
- The question asks you to assume the second part is TRUE: The person with the Bird drives a Van.

2. Case 2 Deduction (Second part TRUE):
- Person X → Pet: Bird and Car: Van

3. Anchor Assignments (Clues 4 & 5):
- Clue 4: Carl → Pet: Cat.
- Clue 5: Evan → Car: Hatchback and City: LA.

4. Inter-Layer Elimination:
- Use the Exclusionary Clue 2 (NY city) and Conditional Link Clue 3 (Truck car is not Miami city).
- By tracking all exclusions and the definite assignments from the two layers, you can uniquely place the remaining Person, Car, Pet, and City for Alex.
- The only remaining car for Alex after all other constraints are met is the Truck.

Answer: Truck

bi-conditional, hypothesis-testing, case-based-deduction, advanced-exclusion

Question 5

Five boxes (A, B, C, D, E) are stacked vertically (Position 1 is bottom, 5 is top). Each box is painted a different color from: Blue, Red, Yellow, White, Green. Given information: • Box A is at the bottom (Position 1). • The Green box is at the top (Position 5). • Box C is immediately above Box B. • The box at Position 3 is Yellow. • Box C is not Red. What color is Box D?

Step-by-step Solution:

1. Direct Placements:
- Position 1: Box A (Blue)
- Position 5: Box E (Green)
- Position 3: Yellow

2. Build Complete Stack:

| Position | Box | Color |
|----------|-----|-------|
| 5 | E | Green |
| 4 | D | White |
| 3 | C | Yellow |
| 2 | B | Red |
| 1 | A | Blue |

3. Find Box D:
- Box D is at Position 4
- Its color is White

Answer: White

vertical-layering, stacking, deductive-color-coding

Question 6

Six people live in three different buildings (Tower A, B, C). Each building has 2 floors. Each person has a different profession. Given information: • The Lawyer lives immediately above Rajesh (Tower B, F1) • The Doctor lives on Floor 1 of Tower A. • Karan and Sneha live in the same building (Tower C), and neither is the Engineer. • Priya lives in Tower B, but is not the Architect. • Neha lives on Floor 2 of Tower A. What is Neha's profession?

Step-by-step Solution (Requires 3 Parallel Layering Grids):

1. Establish Building and Floor Positions (Clue 1 & 5):
- Clue 5: Neha is in Tower A, F2.
- Clue 1: Priya (The Lawyer) is in Tower B, F2, immediately above Rajesh in Tower B, F1.

2. Departmental Grouping (Clue 3):
- Karan and Sneha are in Tower C.
- By elimination, the remaining person is Amit, who must be in Tower A.

3. Profession Mapping (Clue 2 & 3):
- Clue 2: Amit (Tower A, F1) is the Doctor.
- Clue 3: Karan and Sneha (Tower C) are NOT the Engineer.
- Deduction: Since Neha is in Tower A (and is not Doctor), and is the only person left in Tower A, Neha must be the Engineer.

Answer: Engineer

vertical-layering, multi-building, inter-building, deductive-3-layer

Question 7

Four people move between four zones (A, B, C, D) during three time slots. Each person is in exactly one zone at any time, and multiple people can be in the same zone. Given information: • At 9 AM: Ankit is in Zone A, Bindu is in Zone B, Chirag is in Zone C, Disha is in Zone D • Ankit moves: Zone A → Zone B → Zone C • Bindu moves: Zone B → stays in Zone B → Zone D • Chirag moves: Zone C → Zone D → Zone A • Disha moves: Zone D → stays in Zone D → Zone B Which zone has exactly two people at 10 AM?

Step-by-step Solution:

At 9 AM (9 AM):
- Ankit → Zone A
- Bindu → Zone B
- Chirag → Zone C
- Disha → Zone D

Movement to 10 AM (10 AM):
- Ankit moves from Zone A to Zone B
- Bindu stays in Zone B
- Chirag moves from Zone C to Zone D
- Disha stays in Zone D

At 10 AM (10 AM):
- Ankit → Zone B
- Bindu → Zone B
- Chirag → Zone D
- Disha → Zone D

Zone Occupancy:
- Zone A: 0 person
- Zone B: 2 people
- Zone C: 0 person
- Zone D: 2 people

Therefore, Zone B has exactly two people at 10 AM.

zone-based, movement, temporal-tracking

Question 8

Six people work in an office building with six floors (numbered 1-6 from bottom to top). Each works in a different department and has a different designation. Given information: • The Manager lives on a floor immediately above the Coordinator. • The person in IT does not work on an even-numbered floor. • Esha works in the department where the Manager works on Floor 1. • The Finance department person works on a floor that is two levels above the person in HR. • The Coordinator is on the floor with the Finance department. What is the designation of the person on Floor 4?

Step-by-step Solution (Requires 3-Layer Deduction Grid):

1. Initial Setup:
- Floors: 1, 2, 3, 4, 5, 6
- Departments: Sales, HR, IT, Finance, Marketing, Operations
- Professions: Manager, Executive, Analyst, Coordinator, Specialist, Officer

2. Core Positional Deductions (Clue 4):
- Let Floor X = Person in HR.
- The Finance department (Dept Y) is on Floor X+2.
- Since HR is on Floor 2, the Finance department is on Floor 4.

3. Integrating Profession (Clue 5):
- The Coordinator is on the floor with the Finance department.
- Therefore, the person on Floor 4 is the Coordinator.

4. Verification with other clues:
- Clue 1: Manager must be on F2 and Coordinator on F1, OR Manager on F4 and Coordinator on F3, etc. This helps place other pairs.
- Clue 2: The person in IT must be on F1, F3, or F5 (odd floors).
- Clue 3: Esha is on F6. They are in the same department as the Manager on F1 (Dept: Sales). This links F1 and F6.

The integration of all these relative clues leads uniquely to the conclusion for Floor 4.

Answer: Coordinator

vertical-layering, 3-layer, profession, deductive-dependency

Question 9

Six people work in three departments with two shift timings across three working days. Each person may work multiple days but only one shift per day. Given information: • **If** a person works the **Evening** shift, **then** they must be in the **HR** department. • Neha works Evening (Evening) shift in Marketing (Marketing) on Wednesday. • No person works Morning (Morning) shift on Friday (Friday) in the Marketing department. • Priya works in HR on Wednesday. If Rohan works in Sales and is on the Evening shift, which department must be the exception to the main conditional rule?

Step-by-step Solution (Requires Rule Exception Analysis):

1. Analyze the Core Conditional Rule (Clue 1):
- Rule: If Shift = Evening, then Department = HR.
- This implies: Any non-HR department cannot have an Evening shift worker.

2. Check the Contradictory Clue (Clue 2):
- Clue 2: Neha (a person) works Evening shift in the Marketing (Marketing) department.

3. Identify the Exception:
- Clue 2 presents a direct contradiction to Clue 1. Since all clues are given as true, the conditional rule must have an unstated exception.
- The person in the Marketing department works the Evening shift, violating the rule that all Evening shifters must be in HR.
- Therefore, Marketing is the implied exception to the Conditional Rule's outcome.

Answer: Marketing

conditional, complex-rules, if-then-exception

Question 10

Six people work in an office building with six floors (numbered 1-6 from bottom to top). Each works in a different department and has a different designation. Given information: • The Manager lives on a floor immediately above the Coordinator. • The person in IT does not work on an even-numbered floor. • Chetan works in the department where the Manager works on Floor 1. • The Finance department person works on a floor that is two levels above the person in HR. • The Coordinator is on the floor with the Finance department. What is the designation of the person on Floor 4?

Step-by-step Solution (Requires 3-Layer Deduction Grid):

1. Initial Setup:
- Floors: 1, 2, 3, 4, 5, 6
- Departments: Sales, HR, IT, Finance, Marketing, Operations
- Professions: Manager, Executive, Analyst, Coordinator, Specialist, Officer

2. Core Positional Deductions (Clue 4):
- Let Floor X = Person in HR.
- The Finance department (Dept Y) is on Floor X+2.
- Since HR is on Floor 2, the Finance department is on Floor 4.

3. Integrating Profession (Clue 5):
- The Coordinator is on the floor with the Finance department.
- Therefore, the person on Floor 4 is the Coordinator.

4. Verification with other clues:
- Clue 1: Manager must be on F2 and Coordinator on F1, OR Manager on F4 and Coordinator on F3, etc. This helps place other pairs.
- Clue 2: The person in IT must be on F1, F3, or F5 (odd floors).
- Clue 3: Chetan is on F6. They are in the same department as the Manager on F1 (Dept: Sales). This links F1 and F6.

The integration of all these relative clues leads uniquely to the conclusion for Floor 4.

Answer: Coordinator

vertical-layering, 3-layer, profession, deductive-dependency

Question 11

Five individuals must be matched to their Car, Pet, and City of residence. No two individuals share any of these attributes. Given information: • **Either** the person with the **Fish** lives in **Chicago**, **OR** the person with the **Dog** drives a **Van**. • The person in **LA** does not own a **Cat** and does not drive a **Truck**. • If a person drives a **Sedan**, their city is not **NY**. • **Carl** is the one who owns the **Cat**. • The person who drives a **SUV** is **Evan**, who is also the one from **Boston**. If you assume the second part of the Bi-Conditional clue (Clue 1) is **true**, what car does Alex drive?

Step-by-step Solution (Requires Case-Based Reasoning):

1. Analyze the Bi-Conditional Clue (Clue 1):
- Clue 1: (Pet=Fish → City=Chicago) OR (Pet=Dog → Car=Van)
- The question asks you to assume the second part is TRUE: The person with the Dog drives a Van.

2. Case 2 Deduction (Second part TRUE):
- Person X → Pet: Dog and Car: Van

3. Anchor Assignments (Clues 4 & 5):
- Clue 4: Carl → Pet: Cat.
- Clue 5: Evan → Car: SUV and City: Boston.

4. Inter-Layer Elimination:
- Use the Exclusionary Clue 2 (LA city) and Conditional Link Clue 3 (Sedan car is not NY city).
- By tracking all exclusions and the definite assignments from the two layers, you can uniquely place the remaining Person, Car, Pet, and City for Alex.
- The only remaining car for Alex after all other constraints are met is the Sedan.

Answer: Sedan

bi-conditional, hypothesis-testing, case-based-deduction, advanced-exclusion

Question 12

Four people move between four zones (A, B, C, D) during three time slots. Each person is in exactly one zone at any time, and multiple people can be in the same zone. Given information: • At 9 AM: Ankit is in Zone A, Bindu is in Zone B, Chirag is in Zone C, Disha is in Zone D • Ankit moves: Zone A → Zone B → Zone C • Bindu moves: Zone B → stays in Zone B → Zone D • Chirag moves: Zone C → Zone D → Zone A • Disha moves: Zone D → stays in Zone D → Zone B Which zone has exactly two people at 10 AM?

Step-by-step Solution:

At 9 AM (9 AM):
- Ankit → Zone A
- Bindu → Zone B
- Chirag → Zone C
- Disha → Zone D

Movement to 10 AM (10 AM):
- Ankit moves from Zone A to Zone B
- Bindu stays in Zone B
- Chirag moves from Zone C to Zone D
- Disha stays in Zone D

At 10 AM (10 AM):
- Ankit → Zone B
- Bindu → Zone B
- Chirag → Zone D
- Disha → Zone D

Zone Occupancy:
- Zone A: 0 person
- Zone B: 2 people
- Zone C: 0 person
- Zone D: 2 people

Therefore, Zone B has exactly two people at 10 AM.

zone-based, movement, temporal-tracking

Question 13

Five individuals must be matched to their Car, Pet, and City of residence. No two individuals share any of these attributes. Given information: • **Either** the person with the **Cat** lives in **LA**, **OR** the person with the **Bird** drives a **SUV**. • The person in **Miami** does not own a **Snake** and does not drive a **Sedan**. • If a person drives a **Van**, their city is not **NY**. • **Carl** is the one who owns the **Snake**. • The person who drives a **Hatchback** is **Evan**, who is also the one from **Boston**. If you assume the second part of the Bi-Conditional clue (Clue 1) is **true**, what car does Alex drive?

Step-by-step Solution (Requires Case-Based Reasoning):

1. Analyze the Bi-Conditional Clue (Clue 1):
- Clue 1: (Pet=Cat → City=LA) OR (Pet=Bird → Car=SUV)
- The question asks you to assume the second part is TRUE: The person with the Bird drives a SUV.

2. Case 2 Deduction (Second part TRUE):
- Person X → Pet: Bird and Car: SUV

3. Anchor Assignments (Clues 4 & 5):
- Clue 4: Carl → Pet: Snake.
- Clue 5: Evan → Car: Hatchback and City: Boston.

4. Inter-Layer Elimination:
- Use the Exclusionary Clue 2 (Miami city) and Conditional Link Clue 3 (Van car is not NY city).
- By tracking all exclusions and the definite assignments from the two layers, you can uniquely place the remaining Person, Car, Pet, and City for Alex.
- The only remaining car for Alex after all other constraints are met is the Van.

Answer: Van

bi-conditional, hypothesis-testing, case-based-deduction, advanced-exclusion

Question 14

Six items (P, Q, R, S, T, U) are arranged in a 2×3 grid (2 rows, 3 columns). Each has a unique color and associated number. Colors: Red, Blue, Green, Yellow, Orange, Purple Numbers: 2, 4, 6, 8, 10, 12 Given information: • Item U is at position (1,1) with number 6. • The item at (2,2) has number 12. • The item at (2,2) is Red colored. • The item with number 8 is in the same column as the Red item. • No item in Row 1 is Red. What item is in Row 2, Column 2?

Step-by-step Solution:

1. Direct Assignments:
- (1,1) = U (Number 6)
- (2,2) = Number 12, Color Red

2. Column Constraints:
- The number 8 is in the same column as Red (Column 2)
- Therefore, either (1,2) or (2,2) has number 8
- Since (2,2) has 12, (1,2) must have number 8

3. Row Constraints:
- Row 1 has no Red items

4. Diagonal Relationship:
- Q is diagonally opposite the Orange item

Final Grid:

| Position | Item | Color | Number |
|----------|------|-------|--------|
| (1,1) | U | Blue | 6 |
| (1,2) | P | Purple | 8 |
| (1,3) | Q | Yellow | 2 |
| (2,1) | T | Orange | 4 |
| (2,2) | S | Red | 12 |
| (2,3) | R | Green | 10 |

Therefore, the item at (2,2) is S.

horizontal-layering, grid-based, 4-layer, relational-matrix

Question 15

Five boxes (A, B, C, D, E) are stacked vertically (Position 1 is bottom, 5 is top). Each box is painted a different color from: Yellow, Blue, Green, White, Red. Given information: • Box A is at the bottom (Position 1). • The Red box is at the top (Position 5). • Box C is immediately above Box B. • The box at Position 3 is Green. • Box D is not Red. What color is Box B?

Step-by-step Solution:

1. Direct Placements:
- Position 1: Box A (Yellow)
- Position 5: Box E (Red)
- Position 3: Green

2. Build Complete Stack:

| Position | Box | Color |
|----------|-----|-------|
| 5 | E | Red |
| 4 | D | White |
| 3 | C | Green |
| 2 | B | Blue |
| 1 | A | Yellow |

3. Find Box B:
- Box B is at Position 2
- Its color is Blue

Answer: Blue

vertical-layering, stacking, deductive-color-coding

Question 16

Five people live on five different floors of a building (numbered 1 to 5 from bottom to top). Each person likes a different color. Given information: • Amit lives on floor 3. • The person who likes Green lives 2 floors away from Vikram. • Priya does not like Yellow and is not on a floor adjacent to Rohan. • The person who likes Blue lives immediately below Amit. Who lives on floor 4?

Step-by-step Solution (Requires Deduction Grid):

1. Establish Knowns and Direct Assignments:
- Clue 1: Amit is on Floor 3 (Floor 3).
- Clue 4: The person liking Blue (Color X) is on the floor immediately below Amit. Since Amit is on Floor 3, the person liking Color X must be on Floor 2.
- This means the person on Floor 3 is Amit, and the person on Floor 2 is the one liking Blue.

2. Resolve Relative Positional Clues (Clue 2):
- Vikram is on Floor 2.
- The person liking Green is on Floor 4 (2 floors away from Vikram). This helps place the color Green on Floor 4.

3. Apply Exclusionary Clue (Clue 3):
- Priya is on Floor 1. We know their color is NOT Yellow (the color on Floor 5). This helps narrow down the color possibilities for Floor 1.
- We also know Priya is NOT adjacent to the target person on Floor 4, which is true as they are on F1.

4. Final Arrangement (Deduction):
By combining the fixed positions (F3 and F2) with the positional link (Clue 2) and the exclusions, the only unique arrangement is:

| Floor | Person | Color |
| :---: | :---: | :---: |
| 5 | Sneha | Yellow |
| 4 | Rohan | Green |
| 3 | Amit | Red |
| 2 | Vikram | Blue |
| 1 | Priya | White |

Answer: Rohan

vertical-layering, floor-puzzle, deductive-2-layer

Question 17

Five people live on five different floors of a building (numbered 1 to 5 from bottom to top). Each person likes a different color. Given information: • Priya lives on floor 3. • The person who likes Red lives 3 floors away from Sneha. • Sneha does not like White and is not on a floor adjacent to Amit. • The person who likes Yellow lives immediately below Priya. Who lives on floor 4?

Step-by-step Solution (Requires Deduction Grid):

1. Establish Knowns and Direct Assignments:
- Clue 1: Priya is on Floor 3 (Floor 3).
- Clue 4: The person liking Yellow (Color X) is on the floor immediately below Priya. Since Priya is on Floor 3, the person liking Color X must be on Floor 2.
- This means the person on Floor 3 is Priya, and the person on Floor 2 is the one liking Yellow.

2. Resolve Relative Positional Clues (Clue 2):
- Sneha is on Floor 1.
- The person liking Red is on Floor 4 (3 floors away from Sneha). This helps place the color Red on Floor 4.

3. Apply Exclusionary Clue (Clue 3):
- Sneha is on Floor 1. We know their color is NOT White (the color on Floor 5). This helps narrow down the color possibilities for Floor 1.
- We also know Sneha is NOT adjacent to the target person on Floor 4, which is true as they are on F1.

4. Final Arrangement (Deduction):
By combining the fixed positions (F3 and F2) with the positional link (Clue 2) and the exclusions, the only unique arrangement is:

| Floor | Person | Color |
| :---: | :---: | :---: |
| 5 | Rohan | White |
| 4 | Amit | Red |
| 3 | Priya | Blue |
| 2 | Vikram | Yellow |
| 1 | Sneha | Green |

Answer: Amit

vertical-layering, floor-puzzle, deductive-2-layer

Question 18

Six people work in two companies. Each company has multiple departments, and each department has multiple teams. Given information: • TechCorp has two departments: Engineering and Sales • InnoSoft has two departments: Marketing and HR • Engineering has Team Alpha and Team Beta • Sales has only Team Gamma • Marketing has only Team Delta • HR has Team Epsilon and Team Zeta • Anil is in Team Alpha, Bina is in Team Beta • Chirag works in Sales department of TechCorp • Divya is in Marketing department of InnoSoft • Esha and Farhan are in HR department, in different teams In which company does Esha work?

Step-by-step Solution:

Layer 1: Company Structure
Two companies: TechCorp, InnoSoft

Layer 2: Department within Company

TechCorp Departments:
- Engineering
- Sales

InnoSoft Departments:
- Marketing
- HR

Layer 3: Teams within Departments

TechCorp → Engineering:
- Team Alpha
- Team Beta

TechCorp → Sales:
- Team Gamma

InnoSoft → Marketing:
- Team Delta

InnoSoft → HR:
- Team Epsilon
- Team Zeta

Layer 4: Individual Assignment

TechCorp:
- Engineering → Team Alpha → Anil
- Engineering → Team Beta → Bina
- Sales → Team Gamma → Chirag

InnoSoft:
- Marketing → Team Delta → Divya
- HR → (HR teams) → Esha, Farhan

Nested Integration:
Esha is in HR department.
HR department exists only in InnoSoft.
Therefore, Esha works in InnoSoft.

Answer: InnoSoft

nested-layers, hierarchical, company-dept-team, ultra-complex

Question 19

Five individuals must be matched to their Car, Pet, and City of residence. No two individuals share any of these attributes. Given information: • **Either** the person with the **Snake** lives in **LA**, **OR** the person with the **Cat** drives a **Hatchback**. • The person in **Miami** does not own a **Fish** and does not drive a **Sedan**. • If a person drives a **Van**, their city is not **Boston**. • **Carl** is the one who owns the **Fish**. • The person who drives a **SUV** is **Evan**, who is also the one from **Chicago**. If you assume the second part of the Bi-Conditional clue (Clue 1) is **true**, what car does Alex drive?

Step-by-step Solution (Requires Case-Based Reasoning):

1. Analyze the Bi-Conditional Clue (Clue 1):
- Clue 1: (Pet=Snake → City=LA) OR (Pet=Cat → Car=Hatchback)
- The question asks you to assume the second part is TRUE: The person with the Cat drives a Hatchback.

2. Case 2 Deduction (Second part TRUE):
- Person X → Pet: Cat and Car: Hatchback

3. Anchor Assignments (Clues 4 & 5):
- Clue 4: Carl → Pet: Fish.
- Clue 5: Evan → Car: SUV and City: Chicago.

4. Inter-Layer Elimination:
- Use the Exclusionary Clue 2 (Miami city) and Conditional Link Clue 3 (Van car is not Boston city).
- By tracking all exclusions and the definite assignments from the two layers, you can uniquely place the remaining Person, Car, Pet, and City for Alex.
- The only remaining car for Alex after all other constraints are met is the Van.

Answer: Van

bi-conditional, hypothesis-testing, case-based-deduction, advanced-exclusion

Question 20

Six items are placed on six shelves (1=bottom, 6=top). Each item has a unique color and is Small, Medium, or Large (exactly two of each). No two adjacent shelves have the same size. Items: Book, Vase, Clock, Frame, Lamp, Trophy Colors: Red, Blue, Green, Yellow, Black, White Given information: • The item on Shelf 6 is Small-sized. No two adjacent shelves have the same size. • The item on Shelf 3 is White colored. • The Red item is on Shelf 2, which is 3 shelves below the Frame. • The Medium-sized item is the Book. • The item on Shelf 1 is not Green. What item is on Shelf 4?

Step-by-step Solution:

1. Size Pattern (Clue 1):
- Shelf 6: Small
- No adjacent same size + exactly 2 each → sizes forced:
- S6: Small
- S5: Large
- S4: Medium
- S3: Large
- S2: Medium
- S1: Small

2. Positional Relationship (Clue 3):
- The Red item is on Shelf 2
- Shelf 2 is 3 shelves below Shelf 5
- Therefore, Shelf 5 has the Frame item

3. Size-Item Link (Clue 4):
- The Medium-sized item is the Book
- Shelf 4 is Medium-sized
- Therefore, Shelf 4 contains the Book

Complete Arrangement:

| Shelf | Item | Color | Size |
|-------|------|-------|------|
| 6 | Lamp | Black | Small |
| 5 | Frame | Yellow | Large |
| 4 | Clock | Green | Medium |
| 3 | Trophy | White | Large |
| 2 | Book | Red | Medium |
| 1 | Vase | Blue | Small |

Answer: Clock

vertical-layering, categorical, non-adjacency-constraints

Multi-Layer Puzzles - Beginner Level: multi-dimensional puzzles BEGINNER

What you'll learn in this worksheet:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20