How to solve high level box positioning reasoning puzzle for SBI PO quickly 9 | SureSolv

How to solve high level box positioning reasoning puzzle for SBI PO quickly 9

Go on forming, enlarging and fitting bonded member structures onto the main logic table

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

In this ninth tutorial session, while solving a high level box positioning reasoning puzzle, we will be largely involved in detailed logic analysis on formation and placement of temporary bonded member structures onto the main logic table to achieve the breakthroughs.

Additionally, strategic and tactical selection of logic condition statements at each stage as well as compact representation of the logic table do always play important part in successful solution of such high level reasoning puzzles in quick time.

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

  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.
  2. The box containing Cherry Marble is kept immediately below wooden box and is made up of same material as T.
  3. Box S is kept somewhere between W and X and X being below S.
  4. The two cardboard boxes are kept vertically adjacent to each other.
  5. Cappuccino cake is kept exactly between V and the box containing Milk Chocolate.
  6. X doesn’t contain Pineapple cake.
  7. Box U is kept three places below box W which is kept immediately below the box containing Cherry Marble cake.
  8. The box containing Raspberry cake is placed at even numbered place but is not placed at the bottom.
  9. The steel box kept at top contains Pineapple or Chocolate Almond cake.
  10. Box U is not made up of cardboard.
  11. V which contains Black Forest cake is made up of wood.
  12. The box containing Butter White cake is made up of wood.
  13. S doesn’t contain any of Pineapple or Raspberry cake.

Questions

Question 1. Which box contains Cappuccino cake?

  1. S
  2. R
  3. W
  4. U
  5. P

Question 2. Which are the boxes made of cardboard?

  1. X and R
  2. W and S
  3. W and P
  4. X and S
  5. W and R

Question 3. Which of the following combinations is correct?

  1. X, Butter White, wood.
  2. X, Cappuccino, wood.
  3. U, Milk Chocolate, steel.
  4. S, Chocolate Almond, plastic.
  5. P, Cherry Marble, Steel.

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

  1. V
  2. P
  3. U
  4. R
  5. T

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

  1. T
  2. X
  3. P
  4. U

Solution to the four variable high level Box positioning reasoning 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 positions, eight contents and four materials of boxes potentially make the problem difficult.
  • Overall logic condition analysis immediately revealed predominance of formation of bonded member structures.
  • 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.

how-to-solve-high-level-box-positioning-puzzle-9-logic-table

Solution Stage 1: First condition selection

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.

The statement 9 only provides direct assignment of some value, but continuing further with respect this first placement we find statement 1 providing further certain placement of members.

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 material is fixed as wood by statement 9, by statement 1, T of plastic can only be placed at position 2, and R two places below it at position 4.

Finding no other certain placements,

  1. 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.
  2. 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 resides Cherry Marble cake by the same statement. It is a five position bonded member structure. Then linking Cherry Marble with wooden box above it, statement 2 enlarges the bond to a six-position bonded member structure.

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

Breakthrough in placement of bonded member structure

The six position high bonded member structure is recorded in the temporary work area below the main logic table. Wood below plastic and W below R is the only way we can place the bonded structure onto the main logic table. The logic table after this certain placement is shown below. This provides the first major breakthrough.

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

Solution Stage 2: Preparing the second group of bonded structures

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 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 place high 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 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

Sensing possible difficulties in certain placement with only these two structures, we decide to create one more two member adjacent structure by statement 4 (two cardboard boxes vertically adjacent). In addition U having fixed position now, we execute Statement 10 to create no cardboard condition for U. It means, together all these will be in a quite restricted environment and possibility of certain placement through conflict will increase.

We don't see through all the next logic steps, but we are just following methods and creating situations where certain placements are highly likely.

More so, because the rest of the statements don't hold much information for a major breakthrough.

Managerially (or strategically) thinking, this is the most preferred situation.

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 temporary bonded structures for further analysis.

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

Solution Stage 2: Detailed logic analysis to resolve placement of the bonded member structures onto the main logic table 

It is easy to see that V cannot be in position 3 as that region crowded. In both configurations there will be conflicts in cakes. So it can be only in position 6 ot 7.

In configuration 2, V in 6 is inavlid because of cake conflict with Cherry Marble, and so in this configuration V can only be in position 7.

In configuration 1, V cannot be placed in position 7 because of shortage of positions for its structures, but it can possibly be placed in position 6. Let us consider this situation bringing in the two cardboards.

In configuration 1, if we place V in position 6, the two cardboard boxes must be placed in position 7 and 8, and as 8 is a no cardboard position, the positioning of V in configuration 1 becomes impossible.

With only possibility of V in configuration 2 and in position 7 remaining valid, we can now merge the bonded structures with the main logic table without any conflict. This is the second major breakthrough.

Solution Stage 2: Logic table status after breakthrough

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

Solution Stage 3: Final certain placements

Position 8 gets material steel by exclusion, as each material is to be used in exactly two boxes, and only steel has been used once and rest are used twice. 

As is the norm, we start a new stage with immediate certain placements. Statement 8 gives us Raspberry as position 2 and Statement 12 gives us Butter White in position 3. 

Statement 8. The box containing Raspberry cake is placed at even numbered place but is not placed at the bottom.
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 S is kept somewhere between W and X and X being below S.

But in the nearly full table, X goes to 3 and S to 1, the top. By exclusion the box P gets position 6. To resolve the only uncertainty of cake in position 1 and 8 we process Statement 13.

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

As S can't have Pineapple in it, Chocolate Almond goes to position 1 and Pineapple to position 8.

The final solved logic table is shown below.

how-to-solve-high-level-box-positioning-puzzle-9-stage-3

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

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.

Takeaways

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.

Analytical approach examples

The whole solution process consists of a number of examples of analytical approach.

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.


Reading list on SBI PO and Other Bank PO level Reasoning puzzles

Tutorials

How to solve SBI PO level logic puzzles in a few simple steps 1

How to solve SBI PO level logic puzzles in a few simple steps 2

How to solve SBI PO level family relation problems in a few simple steps 3

How to solve SBI PO level floor stay Reasoning Puzzle in a few confident steps 4

How to solve high level circular seating reasoning puzzles for SBI PO in confident steps 5

How to solve high level hard two row seating reasoning puzzles for SBI PO in confident steps 6

How to solve high level  circular seating arrangement reasoning puzzles for SBI PO quickly 7

How to solve high level circular seating reasoning puzzles for SBI PO quickly 8

How to solve high level box positioning reasoning puzzle for SBI PO quickly 9

Solved reasoning puzzles SBI PO type

SBI PO type high level floor stay reasoning puzzle solved in a few confident steps 1

SBI PO type high level reasoning puzzle solved in a few confident steps 2

SBI PO type high level reasoning puzzle solved in a few confident steps 3

SBI PO type high level circular seating reasoning puzzle solved in confident steps 4

SBI PO type high level hard reasoning puzzle solved in confident steps 5

SBI PO type high level one to many valued group based reasoning puzzle solved in confident steps 6

SBI PO type high level hard two in one circular seating reasoning puzzle solved in confident steps 7

SBI PO type hard facing away circular seating reasoning puzzle solved in confident steps 8

SBI PO type high level four dimensional reasoning puzzle solved in confident steps 9

SBI PO type hard two row seating reasoning puzzle solved in confident steps 10

SBI PO type high level floor stay reasoning puzzle solved in confident steps 11

Solved reasoning puzzles Bank PO type

Bank PO type two row hybrid reasoning puzzle solved in confident steps 1

Bank PO type four variable basic assignment reasoning puzzle solved in a few steps 2

Bank PO type basic floor based reasoning puzzle solved in a few steps 3

Bank PO type high level floor stay reasoning puzzle solved in quick steps 4