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

First form the family and then the circular seating with profession in the reasoning puzzle for SBI PO

A circular seating puzzle mixed together with a family relations puzzle forms this tough reasoning puzzle for SBI PO solved systematically in easy steps.

In this complex hybrid reasoning puzzle, determine the profession and the identity of the person sitting at each of the 8 positions on a circular table from the 14 given conditions. The 8 persons are related together in a single family.

For detailed concepts on the fundamental techniques and strategies used in solving this type of logic puzzles you should refer to our tutorial sessions with links given at the end.

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

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Reasoning puzzle for SBI PO 7: Family members sitting on a Circular table: Who is related to whom, sits in which place and is in which profession?

Problem description

Eight persons in a family A, B, C, D, E, F, G and H are sitting around a circular table facing the center. Among them there are three doctors, two Engineers, two Authors and one Painter. Each person has only one occupation.

Conditional statements

1. There are three married couples in the family and no unmarried female.
2. Three generation are there in the family.
3. D has two children.
4. G and H are children of E and C respectively.
5. F is wife of D and mother of B and A.
6. C is a female but not wife of A.
7. G, a grandson of D, sits exactly between C and A and only E sits exactly between B and F.
8. Only one person sits between C and B but he is not H.
9. B is not the immediate neighbor of G, who is not opposite to D.
10. B does not sit opposite to a female.
11. One of the sons of D is on immediate left of D.
12. The person who is on the immediate left of G and the person who is on the immediate right of B are not Doctors.
13. The immediate neighbors of E are neither an Engineer nor a Doctor.
14. H is a Painter.

Questions

Question 1. Who among the following sits exactly between D and E?

1. Author
2. Doctor
3. Engineer
4. Painter
5. None of the above

Question 2. Which of the following does not form a group?

1. G
2. E
3. C
4. A
5. None of the above

Question 3. Which of the following two members sit adjacent to each other in the arrangement?

1. BH
2. EC
3. HE
4. GA
5. None of the above

Question 4. Who among the following is a son of E?

1. H
2. G
3. C
4. D
5. None of the above

Question 5. Engineer is the profession for which of the following?

1. D
2. C
3. H
4. Both 1 and 3
5. Both 1 and 2

Note: Try to solve the problem yourself before going through the solution.

Solution to Reasoning puzzle for SBI PO 7: Family members sitting on a Circular table

The very first problem we need to solve is to form the family structure by defining all the relations between the eight members. This is critical information needed at the time of answering the questions and also to solve the circular seating puzzle in the second part of the problem. To avoid mixing up the two puzzles put together into one, our objective will then be to first,

1. Form a family structure representation, and
2. Identify and analyze the family relation defining statements to form the family relations fully.

After forming the family only we will take up the circular seating part of the problem.

In the circular seating reasoning part of the problem, a family of 8 members with 4 professions are sitting around a circular table governed by a set of logic conditions. The professions being less in number than 8, it forms a one to many relationship. We will deal with this specialty by the mechanism of repeating the profession values in the control list of profession values as we had done in the previous puzzle solution.

Solution to Reasoning puzzle for SBI PO 7 on Family and Circular seating: Part 1: Forming the family tree

As there are three generations in the family (which we learn from problem description) we will put the family members into three levels one each for a generation. All members in same generation will be placed on the same level.

Each of the generation levels will be represented by two coupled rows, one will hold the member name and the second cell below it, the relationship status of the member.

At the start, we execute the first part of Statement 7. "G, a grandson of D", because this is the only statement that identifies the head of the family, the grandfather, with certainty. After execution of the statement part the logic table looks like,

As a strategy in family formation with multiple generations we always will look for and execute a statement that defines the family head who will be only one in number. In this case we searched for mention of grandfather and in first part of statement 7 we got it. This is application of Family head first strategy as well as Direct assignment first strategy.

Execution of the statement placed D as grandparent at generation 1 and G as grandson at generation 3. Mark that we cannot be sure at this stage whether D is a grandfather or a grandmother.

Following the highly useful link search technique we search next for a statement that refers to either D or G, preferably D, because that will define the family tree growing downwards faster.

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Statement 5. "F is wife of D and mother of B and A." satisfies this condition. This not only places F side by side with D as his wife, also we are now confirmed that D is indeed the grandfather and F the grandmother.

Furthermore, we place B and A at the second generation level without knowing whether they are sons or daughters. Mark that Statement 3. "D has two children." is now superfluous and only confirms results already achieved till now.

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Excess statement test of efficiency

If the strategic sequencing of the statements is efficient with least number of steps to the solution, quite often a few of the intervening statements may turn out to be superfluous with no ability to add to information already obtained. This characteristic can be taken roughly as an indication that the strategic statement execution is going on the right track.

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Now is the time to try to define the places of the other members in the family tree.

Statement 4. "G and H are children of E and C respectively." referring to maximum number of the rest of family members is thus chosen next. This is the maximum certain assignment strategy at work.

Coupled with the information that the family has three married couples, E and C automatically become the spouses of B and A at second generation level, but in no specific order. We are not also able to specify who is husband or wife at this point. Thus E and C are placed side by side with B and A at second generation level with additional information of "G is child of E" enriching relation status of G at third level.

H being the child of C, is placed at generation 3 side by side with G, but we are not able to specify whether H is a daughter or son.

The second part of Statement 1. "...no unmarried female." resolves this problem because H and G having the status of unmarried singles, both must be sons, and not daughters (married females are consumed in three married couples, D, F, A, B, E and C).

With most of the statements on family tree already considered, it is time now to execute the last such Statement 6. "C is a female but not wife of A." which includes uncertainty (that is why we execute it late). But as the family tree is nearly fully specified at this stage, the uncertainty itself becomes useful. This is Direct assignment with uncertainty.

The first part of the statement confirms that C is indeed a wife, and as she is not wife of A she must be wife of B which confirms B as the son. The subtle indication in "not wife of A" hints at A as a son. Otherwise "wife" word should not have been mentioned with A. This is logical deduction in family relation domain.

With this, at the last, E becomes wife of A by exclusion.

The fully defined family tree is as below,

Mark that we have used a simple family tree definition and representation structure and strategically executed the specific logic statements earmarked for family tree definition. Time taken should be as short as possible because statements are only a few.

Now we will take up the second part of the puzzle, that is, assigning the family members to the positions on the circular table along with their professions.

We have used the problem breakdown technique in separating the puzzle into two parts and solving one after the other.

Solution to Reasoning puzzle for SBI PO 7: Part 2 Stage 1: Logic table representation for circular seating

In a circular table seating puzzle, seating position numbers are not important because the seating positions are relative. We need only to define precisely who sits on left or right of whom with all of them facing the center of the table.

As usual such an 8 position round table seating is simulated by a linear row of 8 positions with the only implicit assumption that the end positions of 1 and 8 are adjacent to each other. 8 positions being an even number of positions, we can predetermine the opposite positions for each position and record it against the column label.

A round table with eight positions is shown below.

We will assign the family member as well as the profession of the member to the 8 positions thus placing the Person and Profession as two row labels. This is a perfectly compact column and row representation with each cell of the logic table ultimately to hold a specific certain assignment and no uncertainty.

The list of persons and iterated 8 values of the professions are written at the top of the table to keep track of which value has been assigned and which are left to be assigned.

As there are three Doctors, two Authors and two Engineers, there are correspondingly three Doctor values, 2 Author and 2 Engineer values with 1 Painter value in the list of professions. In this way we deal with one to many relationship between Professions and Persons.

The logic table we will work on is shown below.

Going through the eight statements left for position assignment from Statement 7 to Statement 14, we find that right or left seating references are very few, but sitting exactly between conditions are more.

This indicates that we need to start the logic analysis process with the Strategy of forming bonded member structures, increase the length of such a structure as much as possible, and when it is no longer possible to increase the number of members in the structures so formed, we would place the structures onto any convenient position of the logic table. We can do this because the positions on the round table are relative to each other.

Solution to Reasoning puzzle for SBI PO 7: Part 2 Stage 2: Strategy 1: Form bonded member structures

This is the strategy of Bonded member structure first in circular seating. At the very start we would like to form as many linearly bonded structures of members as possible without any heed to right or left seating directions. To deal with the right or left seating, we will reverse each structure to create a second structure that will represent the second seating direction.

At the outset we won't be able to place such bonded structures onto the round table as we don't know the seating direction. So we will just write the member names in a string from left to right for each bonded structure.

At the start we will select Statement 7. "G, a grandson of D, sits exactly between C and A and only E sits exactly between B and F." as it has maximum capacity of creation of two three member bonds. This is shown below,

Note that we have reversed each of the two bonds, CGA, and BEF to create two new bonds, AGC and FEB so that the four bonds together cover all possibilities of left-right seating combinations. By this Bonded structure reversing technique, all possibilities are comprehensively considered.

Solution to Reasoning puzzle for SBI PO 7: Part 2 Stage 3: Strategy 2: Linking bonded member structures

At this point we identify Statement 8. "Only one person sits between C and B but he is not H." which has the very useful function of joining pairs of bonded structures reducing the number of structures from 4 to 2 and also increasing the length of each structure to full length of eight.

Let use see how this happens in a little more detail.

In the four structures (two of which are just reverse of the other two), a total number of six unique family member names are covered, A, G, C and B, E , F. In this situation when we encounter Statement 8, it refers to a seventh person who sits between C and B the two end members of the two structures thus effectively joining the two to a seven member bond. But who is sitting between C and B? If it is not H, he can only be the eighth member D. This is logic analysis by exclusion.

Thus a seven member bond A, G, C, D, B, E, F is formed as well as its reverse, F, E, B, D, C, G, A.

As positions are relative in a round table (relative position in circular seating property), we append the eighth left out member H to both the bonded structures to form two full length bonded member structures A, G, C, D, B, E, F, H and F, E, B, D, C, G, A, H. The four to two bonded structure formation is shown below.

Being full length structures we can place both these structures now as two possibilities onto the logic table. The logic table with two possibilities is shown below,

Solution to Reasoning puzzle for SBI PO 7: Part 2 Stage 4: Strategy 3: Resolving uncertainty by left-right reference

This is the time to resolve the uncertainty of two possibilities by looking for a statement that refers to left-right seating positions.

We find such a statement in Statement 11. "One of the sons of D is on immediate left of D." which refers to the left position of D and forces us to refer to the fully defined family tree to find out the sons of D as B and A.

B sits on the left of D in possibility 2, thus satisfying this breakthrough condition and immediately cancelling out the possibility 1.

We show this state as below,

We have just crossed out the first row entries at this step. In the next step we will remove the first row altogether from the table.

At this point the family members are fully assigned to their right positions on the round table. It is now time to determine their Professions at the next step.

Solution to Reasoning puzzle for SBI PO 7: Part 2 Stage 5: Strategy 4: Direct assignment with certainty first

Statements making direct assignments are always given priority but we choose such a statement for the current execution step depending on its degree of uncertainty. In the first stage, if possible, we don't accept any uncertainty in direct assignment statement at all. In subsequent steps we relax this restriction as we have already assigned values which might help to transform an uncertainty into a certainty.

Thus, at every step the primary objective is to achieve certain assignments, one or more than one.

So we look for a statement that assigns a profession to a family member with certainty. The only such statement is Statement 14. "H is a Painter." which puts Painter as profession of H in the logic table with certainty. Accordingly the Painter value is crossed out in the control list of professions at the top of the logic table.

Again we strive to achieve a certain assignment and get one with Statement 13. "The immediate neighbors of E are neither an Engineer nor a Doctor." because Painter value having been already assigned, if Engineer and Doctor values also are removed from consideration, only two Author values are left. Thus by this statement, both F and B in position 1 and 3 get profession as Author.

The logic table after this stage is as below,

At this point only the Statement 12. "The person who is on the immediate left of G and the person who is on the immediate right of B are not doctors." is left. As this rules out professions of C and D as doctors, their profession must be Engineers by negation and exclusion.

Lastly, the professions of rest of the family members, E, G and A must be Doctors by exclusion again.

The fully assigned logic table is shown below,

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Excess superfluous statements that are only confirmatory

Again we find two statements, Statement 9. "B is not the immediate neighbor of G, who is not opposite to D." and Statement 10. "B does not sit opposite to a female." turning out to be of no practical use except for confirming existing assignment information which they do.

This broadly indicates the high efficiency of the strategic analytical solution process.

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We are now ready to answer the questions but we will need to refer to this fully assigned logic table along with the fully defined family tree for answering.

Answers to the questions

Question 1. Who among the following sits exactly between D and E?

Answer 1. Option 1: Author.

Question 2. Which of the following does not form a group?

Answer 2. Option 3: C. The other three E, G, A are Doctors, but C is an Engineer. One needs to be careful while answering such type of questions when multiple differentiating attributes such as Gender and Odd-Even table position are present.

Question 3. Which of the following two members sit adjacent to each other in the arrangement?

Answer 3. Option 4: GA. Among the four specified option values BH, EC, HE and GA, only GA pair sits adjacent on the table.

Question 4. Who among the following is a son of E?

Answer 4. Option 2: G. To answer this question we need to refer to the family tree at last.

Question 5. Engineer is the profession for which of the following?

Answer 5. Option 5: Both 1 and 2. As D and C at Option 1 and 2 are both Engineers, both these options are valid and equivalent, and so cannot be the single valid answer (as per the constraint of multiple choice questions in general). When we identify the Option 5 to cover both the Option 1 and 2, it becomes the single answer more pertinent than the other two options.

An alternate approach in solving this awkward hybrid problem might be to avoid defining the family tree first and refer to the family defining statements only when required for profession and position assignment and when answering the questions.

Overall we call this strategic analytical methodology for solving reasoning puzzles of any kind as the Collapsed column logic analysis technique.

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Recommendation

You need to carefully go through these sessions for absorbing the concepts well, and more importantly you must solve a number of such problems of various types for solving such a problem or its variation in the actual test confidently.

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.

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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.

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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 nine position circular seating easoning 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

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

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

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Solved reasoning puzzles Bank PO type

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