📦 Box Based Puzzles - Basic
Learn box and stack arrangement puzzles - numbered positions, above/below relationships, gap calculations
Box Based Puzzles - Basic
Box puzzles (also called Stack puzzles) involve arranging boxes or items in a vertical stack from bottom to top. Each position in the stack is assigned to a person or an item based on given conditions.
Understanding Box Arrangement
In a box puzzle with 8 boxes:
- The bottommost box is at position 1
- The topmost box is at position 8
- Boxes are arranged in a single vertical column
Convention: Unless stated otherwise, always number from bottom = 1 to top = N. Some questions may specify "top = 1" — read carefully.
Key Terminology
| Phrase in Question | Meaning |
|---|---|
| "A is above B" | A's position number > B's position number |
| "A is below B" | A's position number < B's position number |
| "A is immediately above B" | A is exactly one position above B (A = B + 1) |
| "A is immediately below B" | A is exactly one position below B (A = B - 1) |
| "N boxes between A and B" | There are exactly N positions separating A and B |
| "A is at the top" | A is at the highest position |
| "A is at the bottom" | A is at position 1 |
| "A is 3 positions above B" | A's position = B's position + 3 |
Gap Calculation Formula
The gap (number of boxes between two positions) is calculated as:
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Box Based Puzzles - Basic
Box puzzles (also called Stack puzzles) involve arranging boxes or items in a vertical stack from bottom to top. Each position in the stack is assigned to a person or an item based on given conditions.
Understanding Box Arrangement
In a box puzzle with 8 boxes:
- The bottommost box is at position 1
- The topmost box is at position 8
- Boxes are arranged in a single vertical column
Convention: Unless stated otherwise, always number from bottom = 1 to top = N. Some questions may specify "top = 1" — read carefully.
Key Terminology
| Phrase in Question | Meaning |
|---|---|
| "A is above B" | A's position number > B's position number |
| "A is below B" | A's position number < B's position number |
| "A is immediately above B" | A is exactly one position above B (A = B + 1) |
| "A is immediately below B" | A is exactly one position below B (A = B - 1) |
| "N boxes between A and B" | There are exactly N positions separating A and B |
| "A is at the top" | A is at the highest position |
| "A is at the bottom" | A is at position 1 |
| "A is 3 positions above B" | A's position = B's position + 3 |
Gap Calculation Formula
The gap (number of boxes between two positions) is calculated as:
Gap = |Position of A - Position of B| - 1
Examples:
- A at position 7, B at position 3: Gap = |7 - 3| - 1 = 3 boxes between them
- A at position 5, B at position 4: Gap = |5 - 4| - 1 = 0 boxes (they are adjacent/immediately above-below)
- A at position 8, B at position 1: Gap = |8 - 1| - 1 = 6 boxes between them
Solved Example: 8 Boxes, 8 Persons
Question: Eight persons A, B, C, D, E, F, G, and H have boxes stacked one above the other (bottom = position 1, top = position 8).
Conditions:
- D is placed at position 5
- There are 3 boxes between D and A
- B is immediately above A
- C is above D
- There are 2 boxes between C and G
- F is immediately below E
- H is at position 4
Solution:
Part A - Analysis:
Definite: D = position 5, H = position 4 (conditions 1 and 7)
From (2): 3 boxes between D(5) and A.
- A could be at 5 + 3 + 1 = 9 (impossible, max is 8) or 5 - 3 - 1 = 1
- So A = position 1
From (3): B is immediately above A(1), so B = position 2
From (4): C is above D(5), so C is at position 6, 7, or 8
From (6): F is immediately below E, so F and E are consecutive with E on top
- Possible pairs: (F=3, E=?) — but we need to find where F-E fit
Remaining positions: 3, 6, 7, 8 for C, E, F, G
From (5): 2 boxes between C and G
- If C = 6, G could be at 6+3=9 (no) or 6-3=3. So G = 3
- If C = 7, G could be at 10 (no) or 4 (taken by H). Not possible.
- If C = 8, G could be at 11 (no) or 5 (taken by D). Not possible.
So C = 6, G = 3
Remaining: E and F at positions 7 and 8. From (6): F is immediately below E. So F = 7, E = 8
Final Arrangement:
| Position | Person |
|---|---|
| 8 (Top) | E |
| 7 | F |
| 6 | C |
| 5 | D |
| 4 | H |
| 3 | G |
| 2 | B |
| 1 (Bottom) | A |
Important Concepts
"Above" vs "Immediately above":
- "A is above B" — A can be anywhere above B (any higher position)
- "A is immediately above B" — A is exactly one position above B (consecutive)
"Between" — always count the boxes IN BETWEEN, not the endpoints:
- If A is at 7 and B is at 3, there are 3 boxes between them (positions 4, 5, 6)
Multiple possibilities: When a condition gives 2+ possible positions (e.g., "3 boxes between A and B"), you may need to try both and see which one is consistent with remaining conditions.
Approach Strategy for Box Puzzles
- Draw the grid first — always draw positions 1 to N vertically
- Place definite positions — anyone whose exact position is given
- Calculate gap-based positions — use the gap formula to find possible positions
- Check "above/below" constraints — eliminate impossible positions
- Place "immediately above/below" pairs — these are consecutive, treat as a unit
- Fill remaining by elimination — last persons go in last available slots
Common Traps
- Forgetting the -1 in gap calculation: "3 boxes between" means 3 positions in the gap, not 3 positions apart. |A - B| = 4, not 3.
- Mixing up top and bottom: Some questions start counting from top. Read the question setup carefully.
- "Just above" vs "above": "Just above" = immediately above (adjacent). "Above" = anywhere higher.
- Circular reasoning: Don't assume a position is fixed when it's still a possibility. Try both options.
Speed Tips
- For 8-box puzzles, draw the grid with numbers 1-8 on rough paper immediately
- Use initials only (A, B, C) — never write full names
- When conditions mention a pair (like "F is immediately below E"), draw them as a unit: E over F and move the unit together
- Practice calculating gaps mentally: |Position difference| - 1 = gap