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

Submitted by Atanu Chaudhuri on Thu, 04/05/2017 - 19:39

Strategic logic analysis and sequencing in efficient solution of the hard two row seating reasoning puzzle

sbi po type two row seating reasoning puzzle in confident steps 10

In this session while solving a fairly complex two row three object set seating reasoning puzzle of SBI PO level, step by step systematic and quick solution could be achieved mainly by strategic analytical approach in selecting and executing right combination of logic statements at the right time using the minimal compact logic table.

For detailed concepts on the fundamental techniques and strategies used in solving this type of logic puzzles you should refer to our tutorial sessions,

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

Note: Before going through the solution of the problem, try to solve the problem in a suitably timed exercise session.

We will repeat the special characteristics of two row seating arrangement reasoning puzzle once more. If you are already aware of these concepts you may skip the following section.

Characteristics of two row seating arrangement reasoning puzzles

In a two row seating arrangement reasoning puzzle, a group of persons sit in two rows as below,

two row seating arrangement in reasoning puzzles

The top row members face down or south towards the bottom row members who face north or up. In this arrangement the whole group of persons are equally divided into two groups to occupy positions in the two rows equally. In the figure above for example, 12 persons are divided into two groups each with six members. One of the groups sit on the top row positions and the second on the bottom row in such a way that in both rows the members sit at equal distances.

The "equal distances" condition gives rise to the characteristic of one member in a row facing another member in the other row. If not mentioned we will always assume the members seating at equal distances.

The second characteristic of this form of seating arrangement is the linear nature of the arrangement. Because of this, each row has two extreme ends which is not the case for a circular seating arrangement.

The most important characteristic is though the reversing of the left right directional system for the members sitting on the top row facing south. For the members seated on the top row, identifying their left right directions is easy but not for us who look at the figure and try to solve the puzzle. For us it is as if we are facing the top row members and that's why our looking direction is opposite to their direction of looking which determines the left right directional system.

For the top row, the right direction is to the left of us who are looking at the figure. This conflict of directional mechanism of the top row with our natural directional mechanism creates quite a bit of unease and extra effort in our mind in resolving the conflict when it arises in a logic statement.

To resolve this left-right conflict and avoid the extra effort, we adopt a simple system. On encountering a left or right mention for top row in a logic statement, automatically we reverse the right to left and left to right in the statement and then deal with it by our natural directional system.

In basic form of this type of reasoning puzzle, the persons sit in two rows facing members of the opposite row without any special attribute attached to them. In this form, the puzzle is just a two dimensional assignment logic analysis puzzle, where members are to be assigned to positions.

Observe that all the seating positions together form the primary object set whereas all the members together form the single secondary object set.

Additional specialty in the arrangement is in splitting the two sets equally in two parts. These two parts do not double the number of dimensions but effectively increase the complexity only slightly because of larger number of members of the sets. It is as if the same type of columns and rows are split into two groups.

This duplication of the columns and rows is represented by two sets of similar column and row labels in the logic table representation.

Like any other reasoning puzzle though, the complexity can be increased extensively just by increasing the number of attributes of each member as well as number of members in each set.

With this brief introduction, let us now go into the process of solving a high level two row seating arrangement reasoning puzzle without further delay.

High level Two Row Seating arrangement Reasoning Puzzle for SBI PO

Problem description

In a national conference, six persons Abhi, Bhuvan, Kiran, Rio, Mudra and Nila are sitting in row 1 facing south but not necessarily in the same order and each of them is from a different city among Kolkata, Delhi, Chennai, Mumbai, Pune and Bhopal. Six more persons Juhi, Somu, Vikram, Sonia, Aritra and Meera are sitting in row 2 facing north but not necessarily in the same order and each of them is from a different city among Bengaluru, Cutttack, Patna, Hyderabad, Jammu and Indore. Each person in one row faces exactly one person from the other row.

Conditional statements

Abhi is third from the left end and is opposite to the person who is to the immediate right of the person from Hyderabad.
The person from Hyderabad is opposite to the person who is to the immediate left of the person from Chennai.
The person from Bengaluru and the person from Mumbai sit at right ends in their respective rows.
Kiran is from Mumbai, and sits adjacent to Mudra.
Rio sits opposite to Somu and to the left of Abhi but does not sit at any extreme.
Bhuvan is not adjacent to Rio but opposite to Juhi.
The person from Indore sits neither at an end nor opposite to Abhi, but sits to the right of Juhi.
The person from Patna is adjacent to neither the person from Cutttack nor the person from Jammu.
Sonia sits at an end.
Vikram sits opposite to the person from Delhi but sits at neither end.
Aritra is opposite to the person from Pune and the person from Kolkata is second to the right of the person from Bhopal.
The person from Jammu is not adjacent to Juhi.

Questions

Question 1. Who sits opposite to the person from Bengaluru?

Abhi
Mudra
Bhuban
Kiran
Nila

Question 2. Which of the following five does not belong to the group formed by the rest four?

Juhi-Kolkata
Meera-Delhi
Sonia-Mumbai
Mudra-Cuttack
Rio-Indore

Question 3. Which is the city of the person sitting three positions left of the person from Chennai?

Pune
Kolkata
Delhi
Bhopal
Mumbai

Question 4. Which among the following is a directly opposite sitting pair?

Juhi-Abhi
Meera-Kiran
Aritra-Abhi
Vikram-Nila
Somu-Rio

Question 5. Who are sitting on two sides of the person opposite to Abhi?

Meera-Vkram
Aritra-Sonia
Juhi-Somu
Rio-Bhuvan
Sonia-Juhi

Solution to the Two Row Seating arrangement Reasoning Puzzle of SBI PO type

Problem analysis and representation

We have three sets of objects. The 12 persons in six member two groups, each group from six different cities (a total of 12 cities), are to be assigned to 12 positions in two rows on two parallel long sides of the rectangular table facing each other. The assignment is on one to one basis.

We will duplicate the column labels and row labels for dealing with the two rows of equivalent nature. This is the minimal logic table representation we will work with.

The two object sets Persons and Cities to be assigned to the six positions on both sides will form two sets of row labels and the 12 positions two sets of facing each other column labels. Assignment will be on one to one basis.

As usual, we record list of to-be-assigned objects for each set at the top and in this case bottom of the logic table as well. As a member of an object set is assigned with certainty to a position, we strike it off from its tracking list. This simple mechanism helps us to keep track of the unassigned members of the object sets.

The following is the logic table representation for this problem we will work with. Though position numbers are not important for assigning members to positions, we have numbered the top row starting from 1 at top right position and increasing on the right of the members to 6 in keeping with the directional system of the members of the top row.

sbi po type two row reasoning puzzle solved 10-1

Solution Stage 1: Strategy 1: Direct and certain assignment first with Statements referring to "extreme ends"

In linear seating puzzles, position numbers are not important as the positions are relative, but,

The two extreme ends are vitally important because, any position in a row can be identified with certainty only with reference to the extreme ends.

So at the start (and later also) we look for statement(s) that refer to "extreme ends" (or "right ends", or "left ends") and possibly with the help of other statements can achieve certain placement.

In any assignment puzzle, Direct certain assignments in the beginning is a "highly preferred" priority. Without such a direct certain assignment of a secondary member to a position, we won't be able to place any member onto the logic table in the beginning, and further steps will be difficult to carry out.

To achieve this first certain assignment in a linear seating puzzle, reference to the extreme ends, or right or left ends, explicitly (or implicitly) is a necessity. An example of implicit reference to extreme ends in this two row seating puzzle might be,

Abhi sits on the right of Bhuban with exactly four persons sitting between them.

With this statement, we can place Bhuban at position 1 in top row and Abhi on his right at position 6. These positions are arrived at by first forming a bonded member structure "Abhi-position-position-position-position-Bhuban" (formed according to our natural directional system, reversing "right" in statement to "left") of six position length so that the bonded structure can be placed exactly matching with the six bottom row positions.

In our problem, we locate an explicit reference of "extreme ends" in the form of "right ends" in Statement 3. "The person from Bengaluru and the person from Mumbai sit at right ends in their respective rows.", and straightaway place Bengaluru against bottom row position 12 and Mumbai against position 6 in top row.

Next we look further for a statement that refers to Bengaluru or Mumbai and get it in Statement 4. "Kiran is from Mumbai, and sits adjacent to Mudra." which gives two certain assignments of Kiran in top row position 6 and Mudra in her adjacent position 5.

We have used, Extreme end reference to achieve direct certain assignment first and then used link reference to get another certain assignment.

The following is the logic table after execution of these two statements.

sbi po type two row reasoning puzzle solved 10-2

Solution Stage 2: Strategies: Extreme end search, link reference, easy pickings, favorable zone and positional value conflict with exclusion

Strategic methodological step after first assignment in linear seating puzzles: Continue to look for reference to extreme ends that gives certain assignment

In circular seating puzzles, after the certain assignments in the first stage we look for statements referring to any of the assigned members (as the circular arrangement does not have any ends). But in linear seating puzzle such as this one, we have two ends in each row and so any reference to extreme ends producing certain assignment always remains the highest priority condition to be processed.

In Statement 1. "Abhi is third from the left end and is opposite to the person who is to the immediate right of the person from Hyderabad." we get such a reference and could place Abhi in position 3 and by the second part, Hyderabad against position 9 (opposite position of Abhi is 10, which is Hyderabad's immediate right, and so Hyderabad gets 9).

Note: any reference to extreme ends without producing immediate certain assignment won't get priority.

Easy pickings by link reference

Hyderabad is referred to in Statement 2. "The person from Hyderabad is opposite to the person who is to the immediate left of the person from Chennai." and easily produces the assignment of Chennai against person in position 5.

Favorable zone and conflict of values in occupied positions for placement of vertical bonds

With three positions of row 1 already occupied it tends to be considered as a favorable zone and we look for such an opportunity to use it. In this case, chances of certain placement increases if we try to place a longer bonded structure and better still with additional positional constraints.

We get such an ideal Statement 5. "Rio sits opposite to Somu and to the left of Abhi but does not sit at any extreme." which forms a verical Rio-city-city-Somu bond that could be placed only in position 2 opposite to position 11.

With this assignment, row 1 becomes more favorable with four positions out of six occupied, and as expected we get Statement 6. "Bhuvan is not adjacent to Rio but opposite to Juhi." that places Bhuvan-city-city-Juhi bond in only feasible position 4 and opposite position 9.

Principle of exclusion

With five of six positions in row 1 occupied, sixth member Nila automatically gets assigned to remaining vacant position 1.

The logic table now looks like,

sbi po type two row reasoning puzzle solved 10-3

Solution Stage 3: Strategies: Use of positional constraints, link Search, conflict in favorable zone, and exclusion

Use of Positional Constraints with link search

With row 1 fully occupied, now is the time to look for statements that would mention opposite row members but will also refer to the fully occupied row 1 members so that available position for the opposite row member gets as much restricted as possible.

More are the constraints in occupying a position more is the chance of a certain assignment.

In linear seating a good example of a useful positional constraint is, "sits neither at an end". It immediately reduces feasible positions by 2.

In Statement 7. "The person from Indore sits neither at an end nor opposite to Abhi, but sits to the right of Juhi." we identify three constraints, "sits neither at an end", "nor opposite to Abhi", and most importantly, "sits to the right of Juhi".

Out of three available positions on the right of Juhi two are invalidated leaving only position 11 for Indore.

Again by positional constraint in Statement 12. "The person from Jammu is not adjacent to Juhi." Jammu gets assigned to person in position 7.

Observe that link reference to Juhi played a critical role in this assignment as in the previous one.

Use of Positional Constraints with link search in favorable zone resulting easy pickings

The city row for bottom row persons has turned out to be a vary favorable zone at this point. So we look for any easy pickings.

Statement 8. "The person from Patna is adjacent to neither the person from Cutttack nor the person from Jammu." includes two constraints and a link reference to Jammu. It results in certain assignment of Patna to person in position 10 with little effort. This is an example of easy pickings.

Principle of exclusion

By exclusion, the last unassigned city Cuttack for row 2, goes to the last empty city cell for row 2 against position 8.

The logic table at this stage is shown below.

sbi po type two row reasoning puzzle solved 10-4

Solution Stage 4: Strategies: Use of positional constraints, link Search, vertical bonds, conflict in favorable zone

Positional constraints and vertical bonds

Statement 10. "Vikram sits opposite to the person from Delhi but sits at neither end." includes reference to a vertical bond "opposite to the person from Delhi" as well as includes a constraint "sits at neither end".

This is an interesting elementary logic analysis. Let us explain it in more details.

Out of four available positions 7, 8, 10 and 12 for Vikram, positions 7 and 12 are invalidated by "neither end" clause, but more importantly, even though Delhi is not yet available in the table, when it tried to get a place as a bond opposite to Vikram, we find that city position opposite to position 8 is already occupied. So the only feasible positions for the bond of "Vikram-city-Delhi-person" remains to be position 10 opposite to position 3. In the process Abhi gets Delhi.

In the same way when we select next Statement 11. "Aritra is opposite to the person from Pune and the person from Kolkata is second to the right of the person from Bhopal.", Aritra gets assigned to position 12 and Pune against its opposite position 1.

Use of seating directional reference

Out of two vacant city positions 2 and 4 in row 1, by second part of Statement 11, Kolkata at position 4 is placed on the second position right of Bhopal at position 2.

Use of extreme end reference to resolve two degree uncertainty

Last Statement 9. Sonia sits at an end", places Sonia at position 7 and by exclusion Meera at postion 8.

The logic assignment is complete.

The logic table condition is as below,

sbi po type two row reasoning puzzle solved 10-5.jpg

Now we are ready to answer the questions and it should take only about a minute's time to answer the five questions.

Answers to the questions

Question 1. Who sits opposite to the person from Bengaluru?

Answer 1. Option 5: Nila.

Question 2. Which of the following five does not belong to the group formed by the rest four?

Answer 2. Option 2: Meera-Delhi. All the other four pairs, Juhi-Kolkata, Sonia-Mumbai, Mudra-Cuttack, and Rio-Indore, are the pairs of person and city of opposite person.

Question 3. Which is the city of the person sitting three positions left of the person from Chennai?

Answer 3. Option 4: Bhopal.

Question 4. Which among the following is a directly opposite sitting pair?

Answer 4. Option 5: Somu-Rio. This is the only exactly opposite sitting persons. None of the others, Juhi-Abhi, Meera-Kiran, Aritra-Abhi, Vikram-Nila are opposite sitting pairs.

Question 5. Who are sitting on two sides of the person opposite to Abhi?

Answer 5. Option 3: Juhi-Somu.

As a final comment on this two row reasoning puzzle, though we could solve it smoothly and quickly, it is a puzzle with possibilities of rich learning.

Comment

As before, the adapted compact representation of logic table served us well, but crucial were the strategies in selecting and executing the logic statements so that solution could be reached quickly without any confusion or backtracking.

The ability to adapt the logic table representation for a new type of logic puzzle and more importantly the ability to develop more effective new strategies and techniques of logic condition analysis should result in systematic, assured and quick solution for most types of logic analysis reasoning puzzles.

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 a puzzle was solved.

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.