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

Strategic logic analysis and compact representation adapted for two row seating reasoning puzzles

sbi po level two row seating reasoning puzzle in easy steps 6

In this session we have adapted yet again the collapsed column concept to represent the logic table in minimal form while solving a fairly complex two row seating reasoning puzzle of SBI PO level. However, step by step systematic and quick solution could be achieved mainly by strategic analytical approach in selecting and executing the right combination of logic statements at the right time.

Before going ahead further, you may refer to our other 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 high level floor stay reasoning puzzles for SBI PO in a few confident steps 4

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

In this session we would skip the general theoretical concepts on solving assignment logic puzzles. For understanding the explanations in this session one should go through these basic concepts from the tutorials.


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

Twelve members of a family are sitting on two opposite sides of a rectangular dining table for dinner. Two parallel rows of chairs containing six people each are set in such a way that there is an equal distance between adjacent persons. In row 1, Rio, Bablu, Ruku, Dev, Sonia and Rubai are seated but not necessarily in the same order and all of them are facing south. In row 2, Tukai, Kiran, Mithia, Sindhu, Vivek and Meeni are seated but not necessarily in the same order and all of them are facing north. Each of them likes different food items among, Biriyani, Yakhni, Idli, Korma, Dosa, Poha, Upma, Kebab, Doi Machh, Vada Pav, Pulao and Dhokla, but not necessarily in the same order.

Conditional statements

  1. Ruku, who likes Dosa, sits third to the left of Bablu.
  2. Ruku is not an immediate neighbor of either Sonia or Rio.
  3. Tukai, who likes Pulao, sits third to the right of Sindhu.
  4. Neither Tukai nor Sindhu sits at the extreme ends.
  5. Sonia, who likes Biriyani, faces the one who likes Kebab.
  6. Rubai, who likes Idli, faces Meeni, who sits second to the left of Vivek and does not like Korma.
  7. Vivek is not an immediate neighbor of Sindhu.
  8. Only two people sit between Kiran and Vivek, who like Dhokla and Doi Machh respectively.
  9. Dev likes neither Yakhni nor Korma and sits on the immediate right of the person who likes Dosa.
  10. Rio, who likes Poha, does not face Mithia.
  11. The one who likes Vada Pav sits second to the left of the person who faces the one who likes Idli.

Questions

Question 1. Who sits opposite a person who likes Pulao?

  1. Dev
  2. Bablu
  3. Rio
  4. Sonia
  5. Rubai

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

  1. Kebab
  2. Yakhni
  3. Dhokla
  4. Poha
  5. Vada Pav

Question 3. Which food item is liked by the person sitting two positions left of the person liking Korma?

  1. Biriyani
  2. Idli
  3. Upma
  4. Kebab
  5. Yakhni

Question 4. Which among the following is a valid combination?

  1. Sindhu-Dhokla
  2. Meeni-Poha
  3. Bablu-Yakhni
  4. Mithia-Biriyani
  5. Vivek-Idli

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

  1. Rubai-Bablu
  2. Rio-Rubai
  3. Sonia-Dev
  4. Dev-Bablu
  5. Ruku-Rubai

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 liking twelve different food items 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.

As explained already 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 Food 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 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 level two row seating reasoning puzzle in easy steps 6-1

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" 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, 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 explicitly (or implicitly) is a necessity. An example of implicit reference to extreme ends in this two row seating puzzle might be,

Kiran sits on the right of Vivek with exactly four persons sitting between them.

With this statement, we can place Kiran at position 12 and Vivek on her left at position 7. These positions are arrived at by first forming a bonded member structure "Vivek-position-position-position-position-Kiran" 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 Statement 4. "Neither Tukai nor Sindhu sits at the extreme ends.", but unable to achieve any certain assignment with this condition, we look further for a statement that refers to Tukai or Sindhu.

We find Statement 3. "Tukai, who likes Pulao, sits third to the right of Sindhu." perfectly meets this requirement as it first forms a four position bonded structure of "Sindhu-position-position-Tukai", and when Statement 4 invalidates the extreme ends for both Tukai and Sindhu, this four position "Sindhu-position-position-Tukai" bonded structure along with two invalid extreme ends can be placed perfectly matching with six positions on the bottom row.

Sindhu gets position 8 and Tukai along with Pulao position 11. The corresponding three secondary members assigned (Sindhu, Tukai, Pulao) are struck off from the corresponding tracking lists (for Persons and Food) at the top of the table.

We have used, Extreme end reference, link search and statement group execution to achieve direct certain assignment first.

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

sbi po level two row seating reasoning puzzle in easy steps 6-2

Observe that we have colored the two cells for position 7 and position 12 light orange to indicate that these two cells are out of bounds for both Tukai and Sindhu. We have used the coloring technique as an aid in focusing and analyzing only on the valid cells for the members in question. After we placed the two persons we have removed the colors later.

In actual exam, instead of coloring you can put a pencil cross mark on your scratch paper logic table and after processing is complete can rub off the cross marks.

Solution Stage 2: Strategy 2: Repeated link search, use of bonded member structure and Statement group execution with elementary logic analysis and deduction

Now as we have three assigned members, we look for statements referring to any of the three that may in turn help to achieve a certain assignment. This is link sarch technique in action here.

Only in Statement 7. "Vivek is not an immediate neighbor of Sindhu." we find a reference of Sindhu but not in an immediately productive way. At the moment it just invalidates two empty positions 7 and 9 in row 2 for Vivek leaving only two positions 10 and 12 feasible for him to occupy.

Naturally then we look for any further reference of Vivek that would help us in eliminating one of these two feasible options and would result in a single certain assignment. We find it in Statement 6. "Rubai, who likes Idli, faces Meeni, who sits second to the left of Vivek and does not like Korma." which we need to explain in further details as below.


How to process a compound condition "Rubai, who likes Idli, faces Meeni, who sits second to the left of Vivek and does not like Korma."

The simplest way to deal with any compound condition is to break it up into a series of simple conditions, part by part. This is simplification of compound conditions.

Accordingly, we look at the first part starting with a Subject and stop when we get a single completed meaning of the part.

So we first deal with "Rubai, who likes Idli, faces Meeni" and convert it to a simple three member assignment bond, "Rubai likes Idli and faces Meenie". We can't place it in any position yet.

After taking care of the first part, we form the second part of the compound statement, "Meeni, who sits second to the left of Vivek" and convert it to a simple assertion,

"Meeni sits second to the left of Vivek".

This is important as it forms a three position bonded member structure "Meeni-position-Vivek". Along with the earlier result of two feasible positions 10 and 12 for Vivek, obtained from Statement 7, we now have a certain feasible assignment of Vivek in position 12 and Meeni in position 10.

Because of the three position two member bond formation with Meeni, Vivek can no longer be placed at position 10. It would have created a conflict between already assigned Sindhu and trying to be placed Meeni at position 8.

In our methodology, we attempt a certain assignment as soon as the opportunity arises, and after successful assignment, take the next steps.

With the same objective of achieving immediate certain assignments, we turn our attention back to the converted first part of the compound statement,

"Rubai likes Idli and faces Meeni".

As Meeni has a certain place now, Rubai liking Idli also gets the certain opposite place of position 3. With these steps we exhaust all possibilities of first and second part of the compound statement.

The third and last part of the statement is a simple assignment condition, "Meeni does not like Korma". At this stage we can't get any certain assignment from this negative condition and record it simply as "not Korma" against food item of Meeni.

In summary

We selected Statement 7 as it referred to Sindhu and mentioned Vivek; next we chose Statement 6 as it referred to Vivek; the second part of Statement 6 was processed first as it gave us a certain asignment by three position bond formation and conflict.

It is all strategic statement execution with an objective of maximum certain assignment at the earliest. This forms the maximum certain assigment strategy.

Key concepts used

First link search on Sindhu, next again link search on Vivek, next bonded member structure formation and use and in the process of certain assignment by conflict, statement group execution.

If you are not able to get a certain assignment with one statement, you need to process more linked statements to achieve certain assignments.


All these together form what can be classified as elementary logic analysis and deduction.

After achieving certain placement of Vivek we look again for any left out reference of Vivek and in Statement 8. "Only two people sit between Kiran and Vivek, who like Dhokla and Doi Machh respectively." we get a certain assignment of Kiran to position 9 and by exclusion Mithia to position 7. Additionally , Kiran likes Dhokla and Vivek likes Doi Machh which are placed accordingly. These are easy pickings.

Just remember. such a statement structure as "Only two people sit between Kiran and Vivek" is valuable for achieving certain assignments because it forms the four position bonded structure, "Kiran-position-position-Vivek". As positon of Vivek is already fixed, Kiran automatically gets a fixed location.

The logic table now looks like,

sbi po level two row seating reasoning puzzle in easy steps 6-3

Solution Stage 3: Strategy 3: Link Search technique, Easy pickings and Use of Favorable zone

At any stage we would like very much to process any statement that gives a certain assignment without much effort. We name this strategy as Easy pickings. At the background, link search always works for selecting even an Easy picking statement.

As Easy picking, we locate Statement 11. "The one who likes Vada Pav sits second to the left of the person who faces the one who likes Idli." which refers to a person who faces the one who likes Idli, or in other words, who faces Rubai. As Meeni faces Rubai, we move just two positions left of Meeni and place Vada Pav against Sindhu at position 8. Not a great effort it took as well as the result achieved was not a major one. That's why we classify it under Easy pickings.

But as soon as we form the certain assignment from easy pickings, the food item row for second row members is transformed to a favorable zone. Let us explain what we mean by a favorable zone.

A favorable zone is a row or column of values which is highly occupied and only a few places are left to be occupied.

The reason why it is favorable is, with high occupancy and few values left to be assigned, chances of further success in this zone by processing later conditions should be much higher than any other action.

We know,

There is no absolute certainty for achieving success by any action in this world,

But in real life as well as in solving complex academic problems such as hard logic puzzles, we take important decisions based on things like promising actions, favorable zones and the likes. Usually such an approach bears significantly positive results.

In this case also, with our favorable zone in mind we locate Statement 5. "Sonia, who likes Biriyani, faces the one who likes Kebab." which attracted our attention as it formed a three member vertical bond. Because of the high occupancy in food item row for second row members, this long three member bond could be placed only in position 6 facing position 7.

Looking back we realized that unless we picked the Easy pickings, this success won't have been possible. This result significantly enhanced the importance of Easy pickings to us.

The logic table at this stage is shown below.

sbi po level two row seating reasoning puzzle in easy steps 6-4

Solution Stage 4: Strategy 4: Use of bonded member structure, link search, statement group execution and exclusion

At this last stage, Statement 1. "Ruku, who likes Dosa, sits third to the left of Bablu." enabled us to form a four position bonded member structure, "Bablu-position-position-Ruku" for row 1 but we couldn't place it yet, as the feasible positions for Ruku were two, position 1 and 2.

So by link reference of Dosa, we searched out next Statement 9. "Dev likes neither Yakhni nor Korma and sits on the immediate right of the person who likes Dosa.'" , and this second statement created a right hand neighbor of Ruku as Dev, that made the position 2 invalid for Ruku because of conflict of his right hand neighbor between already placed Rubai and trying to be placed Dev.

We could place Ruku at position 1, Dev at position 2 and Bablu at position 4 with food items Dosa against Ruku at position 1. Against Dev we just noted the two degree negative uncertainty "neither Yakhni nor Korma".

This is use of bonded member structure, link search, and principle of conflict at work.

By Statement 10. "Rio, who likes Poha, does not face Mithia.", the only vacant position 5 at this stage goes to Rio-Poha.

The clause of Statement 10. "does not face Mithia" remained unused.

With Poha struck off from the list of food items, only three food items Yakhni, Korma and Upma remained. We take care of the food item of Dev first as he gets the certain assignment of Upma by cancelling out two of three remaining food items.

This is uncertainty cancellation by a two degree negative uncertainty.

Among the two food items Yakhni and Korma remaining at this point, Meeni does not like Korma, and so Yakhni could be assigned to her with certainty by uncertainty cancellation again.

By exclusion, the last remaining food item Korma goes to Bablu.

The logic assignment is complete.

The logic table condition is as below,

sbi po level two row seating reasoning puzzle in easy steps 6-5 solved

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 a person who likes Pulao?

Answer 1. Option 1: Dev.

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

Answer 2. Option 4: Poha. All the other four are the food items liked by four members sitting in row 2.

Question 3. Which food item is liked by the person sitting two position left of the person liking Korma?

Answer 3. Option 3: Upma.

Question 4. Which among the following is a valid combination?

Answer 4. Option 4: Mithia-Biriyani.

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

Answer 5. Option 2: Rio-Rubai.

Superfluous conditions

Statement 2. "Ruku is not an immediate neighbor of either Sonia or Rio.", and a part of Statement 10. "does not face Mithia" remained unused. In a well-formed logic puzzle every part of logic puzzle need to be used for full assignment.

As a final comment on this two row reasoning puzzle, though we could solve it smoothly and quickly, it is not an easy one by any means.

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.


Tip

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.


You may refer to the following reading list on SBI PO level Reasoning puzzles of various types.

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 high level floor stay reasoning puzzles for SBI PO in a few confident steps 4

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

Solved reasoning puzzles

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

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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

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