Box Puzzle Reasoning Step by Step Easy Solution 9

Submitted by Atanu Chaudhuri on Sun, 17/06/2018 - 17:58

No confusion Solution to Box puzzle reasoning

How to solve box puzzle reasoning 9 for SBI PO level explained step by step using logic table representing box name, position, content cake and material.

Sections are,

The high level box positioning reasoning puzzle with 5 questions.
High level box puzzle reasoning to solve the puzzle: Logic table representation.
Stage 1 of high level box puzzle reasoning solution: First certain assignment, bonded member structure enrichment and first breakthrough by conflict.
Stage 2 of high level box puzzle reasoning solution: Preparing for second group of bonded member structures.
Stage 3 of high level box puzzle reasoning solution: Logic analysis for certain placement of bonded member structures onto main logic table - second breakthrough.
Stage 4 of high level box puzzle reasoning solution: Final solution by straightforward assignment logic and answers to the questions.
Summary with comments and superfluous condition.

For more knowledge and practice you may refer to the list of tutorials and solved reasoning puzzles given at the end.

High level box positioning Reasoning Puzzle for SBI PO

Problem 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.

Conditional statements

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?

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?

Question 5. Which box among the following is two places above the box which contains Cherry Marble?

High level box puzzle reasoning to solve the puzzle

Logic table representation

After going through all the logic conditions briefly, we form our conclusions based on initial problem analysis:

This is essentially a floor based logic puzzle with a few twists, the numbering of floors usually starts from bottom, but here the position numbering starts from top, though the meaning of above, below, top, bottom remain same.
Eight boxes, eight positions, eight contents and four materials of the boxes potentially make the problem difficult.
Overall logic condition analysis reveals predominance of formation of bonded members that are interlinked with each other.
Overall, the breakthroughs will come by trying to place bonded member structures onto the main logic table using positional conflicts.
It won't be an easy problem.

The following logic table will be used for solving the problem.

8 vertical positions form first column and Box name, Cake and Box material form the other three columns. The values of the variables are listed on top of the table as a ready reckoner for tracking assignments.

how to solve high level box positioning puzzle 9 logic table

Solution Stage 1: First condition selection and continued certain assignments using positional constraints and enlarged bonded member structure

As always in the beginning, we search for conditions that provide us maximum number of certain assignments of members onto the empty cells. This is direct assignment first strategy.

Only the statement 9 provides direct assignment of box material steel to position 1 along with content value of two-degree uncertainty that we always accept. Continuing further with respect to this first placement we find statement 1 provides certain placement of two members T and R—overall, a promising result.

Statement 9. The steel box kept at top contains Pineapple or Chocolate Almond cake.
Statement 1. 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.

As the top position box material is steel by statement 9, box T of plastic can only be placed at position 2, and R two places below it at position 4. Position 1 for T is invalid by box material conflict.

Finding no other certain placements,

we look for statements that refer to members separated by a number of positions. This type of statements form bonded member structures and we record these bonded structures in the temporary area below the main logic table.
and we execute statements that refer to members in the bonded structure using link search technique, and enlarge the bonded structures as much as possible. The larger such a bonded structure is, the easier it would be to place it with certainty onto the main logic table along with all its members because of more possibility of positional conflict with existing members of the main logic table.

Together, these strategies form some of the most effective ones in providing crucial breakthroughs in solving high level reasoning puzzles.

The statement 7 is chosen next as it places U three places below W above which is Cherry Marble cake by the same statement. It is a five position bonded member structure with three variable values: U, W and Cherry marble that are in fixed positions with respect to each other.

We don't know their positions in the actual logic table, but at least we are CERTAIN about their positions with respect to each other. That's the most important property of a BONDED MEMBER STRUCTURE.

Furthermore a variable value of the bonded member structure, Cherry marble cake, is referred to (linked) in Statement 2 and helps to increase the size to six-position bond with as many as 5 variable values by a second linking to material Plastic of box T.

This is how a bonded member structure is enlarged and enriched till it can be placed with certainty onto the main logic table. This is a safe strategy that speeds up solution with certainty.

These two statements selected next are shown below.

Statement 7. Box U is kept three places below box W which is kept immediately below the box containing Cherry Marble cake.
Statement 2. The box containing Cherry Marble is kept immediately below wooden box and is made up of same material as T.

The logic table at this stage is shown below.

how to solve high level box positioning puzzle 9 stage 1

Solution Stage 1: Breakthrough in placement of bonded member structure: Box puzzle reasoning

Reasoning: Top two positions in the main logic table are occupied by cake-boxes with materials Plastic below Steel. So the Plastic below Wood in the temporary bonded structure must belong to the second box made of Plastic.

Reasoning: Leaving the top two positions then, six positions from top to bottom are left for the bonded member structure that spans six vertical positions.

This CRITICAL CONSTRAINT FORCES CERTAIN PLACEMENT of the bonded member structure from position 3 to position 8 so that Box R gets Cherry Marble cake content with material Plastic.

This is MERGING of variable values of main table with the temporary bonded structure.

The logic table after this certain placement is shown below.

This provides the first major breakthrough. This has been possible because of the large span of six positions of the bonded structure.

how to solve high level box positioning puzzle 9 stage 1 result

Solution Stage 2: Preparing the second group of bonded structures: Box puzzle reasoning

We have noticed earlier the promising statements 11 and 5 forming a three contiguous position bonded structure based on V. We have not used it earlier as the table was not filled up enough to achieve immediate certain placements.

We decide, now is the time to execute the statements and use these temporary bonded member structures.

Just a reminder: Statement 11 is the only one with all three members in a position assigned to each other, a very valuable one to be used at the right time.

As expected one of the remaining statements, statement 5 refers to one of the members of statement 11 and immediately forms a valuable three vertical position bonded member structure.

Only problem is, the structure can appear with V on top or on bottom, creating two possibilities, not a very easy situation.

Let us show you the two statements and the two possible configurations of the bonded member structures.

Statement 11. V which contains Black Forest cake is made up of wood.
Statement 5. Cappuccino cake is kept exactly between V and the box containing Milk Chocolate.

The two configurations of the bonded structure formed by the two statements are shown below.

how to solve high level box positioning puzzle 9 stage 2 bonds

To be certain of placing one of the two possible configurations in the main table, we must create now more bonded structures.

A convenient two member adjacent structure is formed by Statement 4: two cardboard boxes vertically adjacent.

In addition, existing variable value U is referred to in Statement 10 that also refers to NOT Cardboard box for U. This INCREASES CONSTRAINT IN POSITIONING.

That's the SECOND TECHNIQUE (first being create bonded member structures and go on enlarging till certain placement): INCREASE CONSTRAINT IN POSITIONING IN THE MAIN LOGIC TABLE.

First we'll convert the logic conditions to temporary bonded structure as well as enriched main lofic table.

And then we'll analyze the resulting increased constraint to decide whether certain placement of bonded member structure onto the main table can be made. This is a strategic approach.

Statements 4 and 10 are shown below.

Statement 4. The two cardboard boxes are kept vertically adjacent to each other.
Statement 10. Box U is not made up of cardboard.

We will put together the results of these 4 statements and show the main logic table with three temporary bonded structures for further analysis.

how-to-solve-high-level-box-positioning-puzzle-9-stage-2

Solution Stage 3: Certain placement of bonded member structure onto main logic table: Box puzzle reasoning

Reasoning 3-1: Only three positions 5, 6 and 7 care available for adjacent position TWO cardboard boxes.

Reasoning 3-2: Box V made up of wood cannot be placed in position 6 as it will then break up the three positions 5, 6, 7 into two non-adjacent positions of 5 and 7. The cardboard boxes won't have any feasible positions then.

Reasoning 3-3: So box V can only be placed either in position 5 or position 7.

Reasoning 3-4: But as position 5 is already occupied by box W, BOX V CAN ONLY BE PLACED IN POSITION 7. A certain placement, though partial, is reached as expected.

Reasoning 3-5: Because of three position span of configuration 1 going from top to bottom starting with V and with only two positions available with V at position 7, WE HAVE TO PLACE THE CONFIGURATION 2 bonded member structure with box V at position 7. A complete certain place is achieved.

This is the second major breakthrough and practically solves the problem.

For V the only possible position is then position 7 in configuration 2. So we merge the bonded structures of configuration 2 with the main logic table without any conflict.

Solution Stage 3: Logic table status after breakthrough

Stage 3 box puzzle reasoning 9 placement of bonded member structures

Solution Stage 4: Final solution by straightforward reasoning based on remaining conditions: Box puzzle reasoning

Reasoning 4 -1: Position 8 gets material steel by exception, as each material is to be used in exactly two boxes, and only steel has been used once and rest are used twice.

Now the certain placements.

Statement 8 gives us Raspberry in position 2 as it is the only even numbered position available that is not at the bottom.

Statement 8. The box containing Raspberry cake is placed at even numbered place but is not placed at the bottom.

Similarly, by Statement 12, only free box made up of wood, box at position 3 gets Butter White cake.

Statement 12. The box containing Butter White cake is made up of wood.

Now is the time to take up Statement 3 with high level of uncertainty in floor based problems.

Statement 3. Box X is kept somewhere between W and S and X being below S.

But we have very little uncertainty left in the nearly full table. By Statement 3, X cannot go below W, it must be placed above W and somewhere above it will be S.

We need two free box names above W.

Thus box X gets position 3 and box S gets position 1 with certainty.

Only box name left is box P and free position is position 6. So P gets position 6.

Statement 13 helps to resolve the only uncertainty of type of cake in position 1 and 8,

Statement 13. S doesn’t contain any of Pineapple or Raspberry cake.

As S at position 1 can't have Pineapple in it, out of the two types of cakes, Chocolate Almond goes to position 1 and Pineapple to position 8.

The final solved logic table is shown below.

Stage 4 box puzzle reasoning 9 final solution by straightforward reasoning

The last Statement 6. "X doesn’t contain Pineapple cake." is a verifier statement and is superfluous.

Let us answer the questions now.

Answers to the questions: Box puzzle reasoning

Question 1. Which box contains Cappuccino cake?

Answer 1. Option 5: P.

Question 2. Which are the boxes made of cardboard?

Answer 2. Option 3: W and P.

Question 3. Which of the following combinations is correct?

Answer 3. Option 1: X, Butter White, wood.

Question 4. Which box is exactly between W and X?

Answer 4. Option 4: R.

Question 5. Which box among the following is two places above the box which contains Cherry Marble?

Answer 5. Option 2: T.

Summary with comments and superfluous condition

Overall analysis and main resource identification: From initial analysis of all conditions, main resource to solve the problem was identified as positionally related bonded member structures.

Start of puzzle problem solving: Selection of first condition to process. To speed up the process, positional conflict applied to assign three more assignments at the first stage.

Using positionally related member statements: In case of no direct certain assignment is possible, one must go for creating positionally related or separated bonded member structures and enlarge the bond by additional statements as much as possible. This increases possibility of conflict with existing members in the main logic table resulting in a single possible placement of the bonded member structure. In this problem this strategy played the most important role.

Frequently used and highly effective specific logic analysis techniques: Direct assignment strategy, Link search technique, Conflict analysis, Principle of exclusion, Bonded member structure formation and expansion. For efficiency, bonded structures are recorded in temporary work area.

Condition statement value: Potential certain assignments by direct reference or chain linking references and positionally separated relations are valuable. Statements referring to larger number of parameters in positive context contain higher amount of positive information and so are more valuable.

Comment

The compact representation of logic table is important, but critical is the ability to choose the most effective sequence of executing the logic statements. That is possible only by a well-developed strategy based logic analysis methodology.

To be comfortable with such puzzle solving of any structure and type, there is no alternative other than solving many problems of various types and always analyzing how the puzzle was solved, and learn.

Superfluous conditional statements

A single Statement 6 is superfluous, and it is used for verification of the final assignment. In a way this reflects the efficiency and speed of the solution process.

End note

Solving reasoning puzzles does not need knowledge on any subject—it is just identifying useful patterns by analysis of the problem and using appropriate methods. It improves problem solving skill, because patterns and methods lie at the heart of any problem solving.

Other resources for learning how to discover useful patterns and solve logic analysis problems

Einstein's puzzle or Einstein's riddle

The puzzle popularly known as Einstein's puzzle or Einstein's riddle is a six object set assignment logic analysis problem. Going through the problem and its efficient solution using collapsed column logic analysis technique in the session Method based solution of Einstein's logic analysis puzzle whose fish should be a good learning experience.

Playing Sudoku

As a powerful method of enhancing useful pattern identification and logic analysis skill, play Sudoku in a controlled manner. But beware, this great learning game, popularly called Rubik's Cube of 21st Century, is addictive.

To learn how to play Sudoku, you may refer to our Sudoku pages starting from the very beginning and proceeding to hard level games.