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

Give more time to analysis of logic conditions

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In this seventh tutorial session, while solving a high level circular seating reasoning puzzle, we will be giving more time to analysis of all the logic conditions together. The outcome of this initial analysis will be to form effective strategies for,

  • An overall idea of the nature of the puzzle problem that will help broad level strategies,
  • Selecting the first condition statement which usually is very important for quick final solution, and
  • Deciding the sequence of processing the individual condition statements at later stages which is also critical for quick solution.

At each stage of the puzzle problem solving, the process of evaluation and selection of a specific condition statement that achieves just positive to breakthrough results will be explained.

We repeat—selection of a specific logic condition statement at a specific stage of puzzle problem solving is critically important for smooth and quick solution without confusion. Use of reasoning rules that really work as well will help this selection.

Strategic and tactical selection of logic condition statements at each stage as well as compact representation of the logic table  will play important part in successful solution of such hard reasoning puzzles.

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

We will briefly recap the adapted logic table representation for circular seating arrangement that you may skip if you are familiar with it.


About Circular seating arrangement

In a circular seating arrangement reasoning puzzle, a group of persons sit in a round table as below,

eight-position-circular-seating-arrangement

Any position of the eight can be marked as 1, the next as 2 and so on till 8. Direction of position numbering is not important. It should just be in an increasing sequence. 

Being a round table, only two aspects are important,

  1. Which position is adjacent to which one, and in case of even number of positions,
  2. Which position is opposite to which one.

As you can see, after completing a round from position 1 to position 8, adjacency continues between positions 8 and 1. Position numbering is just a way to express the physical situation. Actual numbering has no particular significance in a circular table.

A third aspect is introduced often in circular seating reasoning puzzles, namely, facing direction of a person. It can either be,

  1. towards center of the table—In, or
  2. away from center of the table—Out. 

Can you guess what does change with change in facing direction?

It is left or right direction. Who is on the right of a facing away person will be different if the person faces towards the center.

Logic table representation

We will represent the eight positions as eight columns and persons and other aspects of a person in rows. For example, if the puzzle is about answering relevant questions about 8 people each of whom likes a different icecream flavor and sits in a round table, we will have eight columns and two rows, one for the persons and the second for the icecream flavors.

While analyzing adjacency or left or right direction, we will assume end position 1 loop back to the other end position 8. We will do it mentally. Representation will remain simple.

If facing away or towards center is involved, we will keep two-directional arrows over the table to remind us that we have to reverse left or right direction if facing direction changes. It is not natural to think this way. One needs practice.

With this brief introduction, we will now take up the main task of solving the hard puzzle that is waiting for our attention.


High level Circular seating Reasoning Puzzle for SBI PO

Problem description

Eight persons namely A, B, C, D, E, F, G and H sit around a circular table facing towards or away from the center. Each of them likes a different icecream flavor, one of the flavors being Strawberry.

The following is what we know about them.

Conditional statements

  1. H’s neighbors face in same direction but opposite to that of H.
  2. G sits third to the left of E who faces towards the center.
  3. D’s spouse who likes Chocolate flavor sits third to the left of D.
  4. C sits third to the right of a man and they face in the same direction.
  5. B’s immediate neighbors face in same direction but opposite to that of B.
  6. The woman who likes Vanilla flavor sits opposite to the man who likes Red Velvet.
  7. A who likes Black Currant flavor sits second to the left of D and they face in the same direction.
  8. The immediate neighbors of C like Vanilla and Mulberry flavors.
  9. B and F sit together and none of them sits with A and D.
  10. G’s spouse who likes Fruit n Nut flavor sits second to the left of G.
  11. The immediate neighbors of H’s only sister who is neither C nor E are A and D.
  12. B who likes Butter Scotch flavor is the only one whose both immediate neighbors are of opposite gender to B.

Questions

Question 1. How many persons face away from the center?

  1. 6
  2. 4
  3. 5
  4. 3
  5. Cannot be determined

Question 2. How many men are there?

  1. 3
  2. 6
  3. 5
  4. 4
  5. Cannot be determined

Question 3. Who likes Strawberry flavor?

  1. G
  2. E
  3. F
  4. H
  5. Cannot be determined

Question 4. Who sits second to the left of C?

  1. A woman
  2. The one who likes Fruit n Nut
  3. G
  4. Both options 1 and 3
  5. Options 1, 2 and 3

Question 5.  Who sits opposite to the one who likes Mulberry?

  1. The one who likes Strawberry 
  2. C
  3. A
  4. H
  5. None of these

Question 6. Who among the following is an immediate neighbor of the one who likes Chocolate?

  1. The one who likes Vanilla
  2. E
  3. The one who likes Red Velvet
  4. C
  5. None of these

Solution to the Circular seating arrangement Reasoning Puzzle of SBI PO level

Logic table representation

To solve this problem, we have to take the condition statements one by one, not necessarily from beginning to end, and try to figure out who sits where, who likes which ice-cream flavor, who is a man or woman and so on. We call this process formally as logic analysis and assignment.

This problem has 5 dimensions to be assigned to each other,

  1. Persons to positions: 8 persons to 8 positions
  2. Icecream flavors to persons: 8 flavors to 8 persons
  3. Gender to persons: 2 genders to 8 persons
  4. Facing direction to persons: 2 facing directions to 8 persons.

To show the assignments in the middle stages and in the final stage, we need a suitable form of representation that is simple, meaningful and has the capacity to hold all information.

We have decided on the following logic table form on which the problem solving process will be carried out in stages.

hard-sbi-po-level-reasoning-puzzle-logic-table.jpg

After we are able to complete all assignments, the table won't have any empty cell.

As at any point every entry in the table will have certainty, we need to transform dual possibilities for a cell such as Persons for Position 2 as B or F, to a certainty and record it in this form in the corresponding cell as "B/F". We accept dual possibilities because such two-degree uncertainties can be resolved by a single contradiction. 

Occasionally, we may need to create Logic table level multiple possibilities. For each such possibility we create a separate version of the table so that in a specific version all cell assignments are certain. This will be clear in the course of solving this present puzzle.

Notice small useful things in the table. All the person names and icecream flavor names are written at the top of the table for keeping track which one is still left. The direction arrows not only remind us about the facing out and in problem, but also help us in resolving such problems. Lastly, the opposite positions are written in bracket beforehand with each position number so that at the time of analysis no time is wasted.

At the beginning of the solution process, we create the table after reading the problem description.

Solution Stage 1: Condition statement analysis

For any reasoning puzzle, you should carefully go through the condition statements to form an overall idea of the problem. Not too much time, but just enough time should be given.

In this problem, the number of conditions is 11 that is fairly large as well as the number of persons and icecream flavors is 8, not quite small. Extra care need to be taken to select the first condition that is to be processed for assignment.

A good reasoning puzzle is to some extent like a maze. With the right first movement you may find next stages smooth and easy.

After scanning the conditional statements we form the opinion that this problem gives more priority to assignment of persons to positions, and so we will consider Persons as the Primary parameter and the rest secondary parameters.

First condition candidate

The general guideline for first condition candidate is, select first the statement that will enable you to make direct and certain assignments to the maximum extent. Statement 2 is the only one by which you can place G and E to two cells in the table with certainty.

As all cells are equivalent at the start in a circular seating representation, at the first assignment we have the freedom to place E at any position and G in 3rd position left of E. We have this freedom only on the first move.

This strategy we call as direct assignment strategy.

In this problem though we go further down the condition list and select Statement 9 as the first statement to be processed.

Statement 9. B and F sit together and none of them sits with A and D.

This statement effectively blocks much more of cells and persons than Statement 2, and so in the spirit of direct assignment we accept it as the statement with maximum direct assignment capacity. We say, it has more effective cell blocking capacity.

We will explain why from the logic table, after we process the Statement 9.

hard-sbi-po-level-reasoning-puzzle-first-condition

Though placement of B or F is not certain, together these two block two cells with certainty creating a Cycle which we prefer. Moreover, it blocks two more cells for two more persons A and D. As it refers to 4 persons, its inormation content is also higher than Statement 2.

Thus after this assignment, A and D have only four cells free to be placed. Naturally then we look for a statement involving A or D now so that further certain assignments take place in this promising situation of two persons to be assigned to four cells. We find A and D together in Statement 7 which we process next.

Statement 7. A who likes Black Currant flavor sits second to the left of D and they face in the same direction.

This strategy we call Link search technique. We use the link of promising set of persons A and D to select Statement 7.

Solution Stage 2: Creating possible options or scenarios

Statement 7 though was promising, there was no way we could avoid creating four possibilities. In actual practice while solving such hard puzzles, invariably we have to create multiple possiblities. Observe that each possibility is certain within itself. Only when a new condition violates one of the possibilities, it is eliminated from consideration, thus reducing number of possibilities, that is, uncertainty.

For each Logic table possibility a separate version  of table is created. In practice we write these combinations in short form, especially so because such possibilities tend to be created in the begining with only a few cells assigned. 

We didn't hesitate in creating these possible options because the patterns contain two Cycles B,F and A,D locked into positions 2,3; 5,7; and 6,8, and are quite stringent, ready to be violated by an oncoming conditional statement. We will talk about Cycles more later. 

We jot down the possibilities generally in short form.

hard-sbi-po-level-reasoning-puzzle-creating-possibilities

Solution Stage 3: Searching for a condition to reduce number of possibilities

As the possibilities were created by A and D, we continue our search using link search technique to identify a statement that mentions A and D.

We find such a statement In Statement 11 which we process next.

Statement 11. The immediate neighbors of H’s only sister who is neither C nor E are A and D.

This statement not only mentions both A and D, it contains mention of no less than 5 persons. This is what we call Information content of a statement.

A general strategy,

The more information a statement contains the more promising it will be in simplifying the current logic assignment status.

Analysis: H's sister sits between A and D. As she can only be one of B, F and G (by elimination or negation, explicit or implicit), and as B and F are locked into two other cells, G is the only possibility left out. So G is the sister of H who sits between A and D. Bonus is the gender of G as a woman.

At this point we recall that G is tied to E in a fixed positional separation arrangement by Statement 2. "G sits third to the left of E who faces towards the centre." With position of G fixed in cell 6 or 7, only valid placements of the two are, E at cell 1 and G at cell 6. Cell 7 is second to the left of E and so Possibilities 3-4 are eliminated at one stroke.

Statement 2 provides the crucial breakthrough in eliminating half of the possibilities.

Statement 2. G sits third to the left of E who faces towards the center.

Let us show the result obtained till now. Two logic table possibilities still remain to be resolved. This is a desirable situation, as we are reducing uncertainty or number of possibility, not increasing it.

hard-sbi-po-level-reasoning-puzzle-reducing-possibilities

Advantage of Cycles, two or more cells blocked by equal number of occupants

We define Cycles as,

Possibility of two or more occupants occupying same number of cells of same level in any order.

A Cycle is created at this stage in Positions (2, 3) by Persons (B, F), who can occupy these two cells in any order but will certainly occupy the two cells between themselves only. No other person can occupy these cells. We are not yet certain Which of B and F will occupy which of cell 2 and 3. This will be made clear by logic analysis in due course of time. But blocking these two cells by B and F, reduces the number of cells from 8 to 6 in our cell assignment analysis efforts.

Because of the power of a Cycle formation, we consider such formation as a "Near certainty" and consider a highly valuable resource for quick solution.

Observe that each of the two logic table possibilities above contains a second Cycle in cells (5, 7) formed by persons (A, D).

Because of the presence of cycles we were comfortable in creating additional logic table formation possiblities, as from experience we know that Cycles have a tendency to get resolved quickly.

In Sudoku game plays of four difficulty levels we needed to deal with extensive and complex logic assignments largely aided by Cycles.

If you want to learn and practice more of logic assignments and useful pattern identification and exploitation, refer to our,

Beginner level Sudoku for first level Sudoku game plays, and Second level Sudoku for medium level Sudoku game plays.

Solution Stage 4: Achieving certainty

With six out of eight positions effectively occupied, only positions 4 and 8 are yet to be occupied by the two remaining persons C and H. Naturally we will process statements with mentions of C and H that will affect position occupation.

This again is an overriding goal or strategy at all stages,

Give more importance to position occupation compared to secondary assignments like icecream flavor, facing direction or gender assignments.

Recall our reference to Primary parameter and secondary parameter.

We identify two statements 1 and 8 with good promise and mention of C or H. As we are in an advanced stage of assignment with not much of major uncertainties left, we will process both the statements together at this stage.

Statement 1. H’s neighbors face in same direction but opposite to that of H.
Statement 8. The immediate neighbors of C like Vanilla and Mulberry flavors.

We won't explain why logic table possibility 1 is eliminated leaving only logic table possibility 2. You find out the shortest reasoning behind this result. Just remember to process the last two statements together, in any order.

Look for our answer to this Task 1 at the end.

hard-sbi-po-level-reasoning-puzzle-achieving-certainty

Solution Stage 5: Using Opposite pair condition

We generally prefer two types of conditions over other types, especially at later stages of analysis. These are,

Opposite pair condition: The phrase, "One person with some characteristics sits opposite to another with some other characteristics" fixes the positions exactly on the table. The final objective of certain assignment will be fulfilled if some of the logic table characteristics are violated leaving certain assignments. At later stages of analysis when logic table is well populated, this Opposite pair condition oftentimes provide the breakthrough.

Fixed positional separation: The phrase, "One person sits third (or second or whatever) on the left (or right) of another person", forms what we call a bonded or tied up structure of two persons (or parameters). At the later stage of analysis, this type of bonded structures come to be quite useful in creating certain assignments because of multiple impacts of fixed separation.

We find Statement 3 refers to fixed positional separation while Statement 6 refers to opposite pair condition. We decide to process both of the statements together at this stage,

Statement 3. D’s spouse who likes Chocolate flavor sits third to the left of D.
Statement 6. The woman who likes Vanilla flavor sits opposite to the man who likes Red Velvet.

Immediately H became D's spouse and we record it for later reference. It would possibly be used later for gender resolution.

The real breakthrough was provided though by the Opposite pair condition in Statement 6. The logic table after this condition processing is given below. It is your task to work out the reasons behind the assignments. Our answer to this Task 2 will be at the end.

hard-sbi-po-level-reasoning-puzzle-using-opposite-pair

With Red Velvet assigned to the person in position 3, we use the ready to assign Statement 12 which resolves the B, F Cycle straighaway by icecream conflict at position 3.

Statement 12. B who likes Butter Scotch flavor is the only one whose both the immediate neighbors are of opposite gender to B.

With only three statements left, we select next, Statement 10 involving a positional separation of G with spouse. It resolves who is G's spouse as well as his gender as a man and icecream as Fruit n Nut. The statement 10 is,

Statement 10. G’s spouse who likes Fruit n Nut flavor sits second to the left of G.

Conflict at position 4, a second candidate for "position second to left of G", determines position 8 as the position for G's spouse, as well as the facing direction of G as Out O, and gender of spouse C as a man M.

Statement 5 falls under category of Easy pickings which easily makes an assignment, but involves no detailed analysis. With such Easy picking you achieve a certain assignment, but usually not more than one. Here we just get the facing direction of B. The Statement 5 is,

Statement 5. B’s immediate neighbors face in same direction but opposite to that of B.

The last Statement 4 though provided us rest of the assignments with some analysis of course. The analysis is your Task 3. Answer will be at the end.

The statement is,

Statement 4. C sits third to the right of a man and they face in the same direction.

With fully assigned logic table as below we are now ready to answer the questions.

hard-sbi-po-level-reasoning-puzzle-resolving-cycle-solved

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

Answers to the questions

Question 1. How many people face away from the centre?

Answer 1. Option 4: 3.

Question 2. How many men are there?

Answer 2. Option 3: 5.

Question 3. Who likes Strawberry flavor?

Answer 3. Option 1: G.

Question 4. Who sits second to the left of C?

Answer 4. Option 4: Both options 1 and 3.

Question 5. Who sits opposite to the one who likes Mulberry?

Answer 5. Option 3: A.

Question 6. Who among the following is an immediate neighbor of the one who likes chocolate?

Answer 6. Option 3. The one who likes Red Velvet.

Takeaways

Overall analysis and logic table representation: Initial overall logic condition analysis, Overall logic analysis strategy formation, Suitable compact logic table representation.

Start of puzzle proble solving: Selection of first condition to process.

General logic analysis strategies: Higher information content more valuable statement, general strategy for selection of first condition to process, Creating possible scenarios, Reducing uncertainty.

Frequently used and highly effective specific logic analysis techniques: Direct assignment strategy, Link search technique, Reducing possible scenarios, Conflict analysis.

Promising positional relations between members: fixed positional seaparation arrangement, Opposite position member, Cycle formation.

Condition statement value: Effective position blocking capacity, Promising positional relations.

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.

Answers to tasks - Elementary logic analysis

Task 1. Stage 4: Reducing uncertainty and number of possible scenarios

In Possibility 1: Statement 1. H’s neighbors face in same direction but opposite to that of H, makes H unable to occupy position 8 as two neighbors (A and E) of member at position 8 are facing opposite directions.

So H is to occupy position 4, the only other vacant position and position 8 is left for C to occupy.

But by Statement 8. The immediate neighbors of C like Vanilla and Mulberry flavors, C also is unable to occupy position 8 as at position 7, the immediate neighbor A likes flavor Black Currant, and not either of Vanilla or Mulberry.

In Possibility 2 no such conflicts exist and C and H can occupy positions 8 and 4 with additional assignments.

Task 2. Stage 5: Using opposite pair

The Statement 6. The woman who likes Vanilla flavor sits opposite to the man who likes Red Velvet, refers to position opposite to position with Vanilla assignment and paiirs it with Red Velvet in its opposite position.

Because of presence of Cycle (Vanilla/Mulberry) between positions 1(5) and 7(3), we will have to consider two Opposite positions 5(1) and 3(7) for Vanilla opposite Red Velvet.

Out of these two 5(1) has already Black Currant assigned (and cannot take in Red Velvet), and so its opposite 1(5) becomes invalid for Vanilla. It gets cycle partner Mulberry and 7(3) gets Vanilla with its opposite 3(7), a man and the Red Velvet.

Task 3. Stage 6: Finishing secondary assignments

Statement 4. C sits third to the right of a man and they face in the same direction, creates two possible positions for the man on whose third to the right is C, namely, position 3(7) and position 5(1) both looking towards the center of the table. Considering their facing direction the man can only be positioned at 5(1) with additional assignments.

The above reasoning falls under the category of Elementary Logic Analysis which some associate with common sense logic. This layer of ability is very important as it forms the foundational skill for higher level logic analysis and general decision making.


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.


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 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

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