8 boxes of cakes of different flavors placed one above another in a stack with each box made from two of four materials. Answer 5 questions using 13 Clues.
Stack of 8 Cake-Box Positioning Reasoning Puzzle
Description
Eight boxes namely P, R, S, T, U, V, W and X are placed from top to bottom not necessarily in the same order. The boxes contain different flavors of cake among Pineapple, Butter White, Cappuccino, Cherry Marble, Black Forest, Milk Chocolate, Chocolate Almond and Raspberry. The boxes are made up of different materials among steel, plastic, wood and cardboard. Each material has exactly two boxes made out of it. Consider top as 1st position.
Clues:
- Box T in two places above R is made up of plastic and both are in the top 4 positions when boxes are arranged from top to bottom.
- The box containing Cherry Marble is kept immediately below wooden box and is made up of same material as T.
- Box X is kept somewhere between W and S and X being below S.
- The two cardboard boxes are kept vertically adjacent to each other.
- Cappuccino cake is kept exactly between V and the box containing Milk Chocolate.
- X doesn’t contain Pineapple cake.
- Box U is kept three places below box W which is kept immediately below the box containing Cherry Marble cake.
- The box containing Raspberry cake is placed at even numbered place but is not placed at the bottom.
- The steel box kept at top contains Pineapple or Chocolate Almond cake.
- Box U is not made up of cardboard.
- V which contains Black Forest cake is made up of wood.
- The box containing Butter White cake is made up of wood.
- S doesn’t contain any of Pineapple or Raspberry cake.
Questions
Question 1. Which box contains Cappuccino cake?
- S
- R
- W
- U
- P
Question 2. Which are the boxes made of cardboard?
- X and R
- W and S
- W and P
- X and S
- W and R
Question 3. Which of the following combinations is correct?
- X, Butter White, wood.
- X, Cappuccino, wood.
- U, Milk Chocolate, steel.
- S, Chocolate Almond, plastic.
- P, Cherry Marble, steel.
Question 4. Which box is exactly between W and X?
- V
- P
- U
- R
- T
Question 5. Which box among the following is two places above the box which contains Cherry Marble?
- S
- T
- X
- P
- U
Solution to Stack of 8 Cake-Box Positioning Reasoning Puzzle: Preparation
Understanding the Objects, their Values and Showing Assignments
It is important to identify the primary object, as all its property values will be assigned to one of the values of the primary object.
- Primary object: Box is not the primary object, its position is.
- Box position from 1 to 8 from right to left with "Right" representing "Up" and "Left" meaning "Down". The directions are shown with the assignment table. Position will be the header of the table.
- Usual vertical representation of assignment table is converted to a horizontal equivalent representation because it is natural for human eye to cover a left to right horizontal pattern more easily than an equivalent vertical pattern.
Secondary objects are the properties of the primary object and will form the rows.
- Box: P, R, S, T, U, V, W, X.
- Cake: Pineapple, Butter White, Cappuccino, Cherry Marble, Black Forest, Milk Chocolate, Chocolate Almond, Raspberry.
- Material: steel, plastic, wood, cardboard: Each box is made up of two materials.
The reasoning puzzle is similar to a floor stay puzzle with many-to-many relationship between Box and Material. This characteristic increases puzzle complexity.
The assignment table at the start.
Simple Clue Analysis Strategy: Forming Implication-list from the Clues First
The Implication list with only the Clue number and its Implications (many of the Clues have more than one implication):
- Clue 1: Horizontal Bond (3-Position): Both to be in the top 4 positions 1 to 4, two probables: (R in 3, T in 1) or (R in 4, T in 2). T is of Plastic.
- Clue 2: Fixed Bond: Cherry Marble-wood Box; Cherry Marble box material is plastic.
- Clue 3: Horizontal Bond: W-?-X-?-S ("?" means unknown number of Positions). For X to be between W and S and below S, W must be below X.
- Clue 4: Fixed Bond: cardboard Box-cardboard Box.
- Clue 5: Horizontal Bond (3-Position): V/Milk Chocolate-Cappuccino-Milk Chocolate/V.
- Clue 6: X not Pineapple.
- Clue 7: Horizontal Bond (5-Position): U-Position-Position-W-Cherry Marble.
- Clue 8: Raspberry in Positions 2, 4 or 6.
- Clue 9: The Box in top Position 1 is steel and has Pineapple or Chocolate Almond.
- Clue 10: U not cardboard.
- Clue 11: Vertical Bond (3-valued): V, Black Forest, wood in same position.
- Clue 12: Butter White and wood in same position.
- Clue 13: S not Pineapple or Raspberry.
Solution to Stack of 8 Cake-Box Positioning Reasoning Puzzle: Clue Analysis
Stage 1: Direct Assignments by a Group of Clues and Two-valued Assignments
Clues 1 and 9 together will provide breakthrough direct assignments.
Clue 1: "R in 4, T in 2 or R in 3, T in 1. T is of plastic."
Clue 9: "Position 1 is steel and has Pineapple or Chocolate Almond."
- Results: Implications of Clue 1 and Clue 9 analyzed together: T cannot be in 1. T in 2, R in 4, plastic in 2. Material steel in Position 1 which has cake "Pineapple or Chocolate Almond."
Clue 7: Horizontal Bond (5-Position): "U-Position-Position-W-Cherry Marble."
- Results: U and W can occupy respectively, either (8 and 5) or (6 and 3).
The stage 1 assignment table:
Stage 2 Breakthrough Assignments: Conflict Created by the 5-Position and Unknown Position Horizontal Bonds
Clue 3: Horizontal Bond: "W-?-X-?-S ("?" means unknown number of Positions)."
- Breakthrough results: W < X < S but, T in 2 blocks X in upward direction—W cannot be in 3, it must be in 5, X in 3 and S in 1.
- With W in 5, by Clue 7, Cherry Marble in 4, U in 8.
Clue 2: Fixed Bond: "Cherry Marble-wood Box; Cherry Marble box material is plastic."
- Results: Cherry Marble box material is plastic, X in 3 is of wood.
Clue 13: "S not Pineapple or Raspberry."
- Result: S in 1 contains Chocolate Almond.
Stage 2 assignment table:
Stage 3 Breakthrough Assignments: By Fixed Bond, Vertical Bond and 3-Position Horizontal Bond
Stage 2 outcome:
- For positions 5, 6, 7, 8 four material options left: cardboard, cardboard, wood and steel.
Clues 4 and 10 together provides a breakthrough assignment.
Clue 4: Fixed Bond: "cardboard Box-cardboard Box."
Clue 10: "U not cardboard."
- Result: If the Fixed Bond of two adjacent cardboards is to be placed among Positions 5, 6 and 7, Position 6 (being common in two probables 7, 6 and 6, 5) must have cardboard.
Clue 11: Vertical Bond: "V, Black Forest, wood same position."
- The only Position free for the vertical bond is Position 7.
- Assignments: V, Black Forest and wood in Position 7; cardboard in Position 6 and 5 (by Clue 4); steel in Position 1 by default; P in 6 by default.
Clue 5: Horizontal Bond (3-Position): "V/Milk Chocolate-Cappuccino-Milk Chocolate/V."
- Results: With V in 2, Cappuccino in 6 and Milk Chocolate in 5.
Clue 8: "Raspberry in 2, 4 or 6."
- Results: With 4 and 6 occupied, Raspberry in 2.
Clue 6. "X doesn’t contain Pineapple cake."
- Results: Out of two cakes left Butter White and Pineapple, X in 2 must contain Butter White and U in 1 contains Pineapple by default.
Completed assignments:
Unused Clue 12 validates the final assignments confirming that the box with Butter White is indeed made of wood.
Answers to the questions
Question 1. Which box contains Cappuccino cake?
- Options: 1:S 2:R 3:W 4:U 5:P.
Answer 1. Option 5: P.
Question 2. Which are the boxes made of cardboard?
- Options: 1:X and R 2:W and S, 3:W and P, 4:X and S, 5:W and R.
Answer 2. Option 3: W and P.
Question 3. Which of the following combinations is correct?
- Options: 1:X, Butter White, wood, 2:X, Cappuccino, wood, 3:U, Milk Chocolate, steel. 4:S, Chocolate Almond, plastic, 5:P, Cherry Marble, Steel.
Answer 3. Option 1: X, Butter White, wood.
Question 4. Which box is exactly between W and X?
- Options: 1:V, 2:P, 3:U, 4:R, 5:T.
Answer 4. Option 4: R.
Question 5. Which box among the following is two places above the box which contains Cherry Marble?
- Options: 1:S, 2:T, 3:X, 4:P, 5:U.
Answer 5. Option 2: T.
Comments
This is hard reasoning puzzle is equivalent to a Floor Stay reasoning puzzle. The solution seemed straightforward because of:
- The simple Clue analysis strategy of forming implication list first and then analyzing only the implications.
- Using concepts and structures of the numerous Bonds between property values—the Horizontal, Fixed and Vertical Bonds.
- Finding and analyzing the Clues giving maximum number of assignments at every step.
The reasoning puzzle is from an SBI PO recruitment test—a difficult one. These puzzles formed an important element for screening young aspirants with quick minds and strong reasoning skills.
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