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

Eight position circular seating arrangement reasoning puzzle solution in easy steps

Adapting logic analysis strategies and logic table representation to solve a circular seating arrangement reasoning puzzle for SBI PO quickly in easy steps.

To solve a hard reasoning puzzle, the first important task is to go through the description of the problem and then the logic conditions quickly and carefully to pick up the key information. On the basis of this first scan you may be able to form a broad strategy for quick solution.

Your second task, that is comparatively simple, is to form the right logic table representation for recording the results of logic analysis. It is important to record all information when you process a specific logic condition.

For circular seating logic puzzle, we use rows for persons and attributes of persons such as direction of facing, gender etc, and 8 columns for the table positions arbitrarily from 1 to 8 for an eight position circular table.

The end positions are mentally treated as adjacent to each other.

The first challenging task in any reasoning puzzle solution, is to select the first statement or group of statements that would give you maximum return in terms of direct certain assignments.

Thereafter you have to use strategies and techniques for processing subsequent logic conditions to follow some kind of method that is not overly complex, and achieve certain assignments of variable values as quickly as possible.

Simplicity of approach as well as assured certain assignments without wasting time are the keys to quick solution of tough reasoning puzzles.

The next logic statement to process will depend more on the present logic assignment state and not on the sequence in which it appears in problem description.

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

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About Circular seating arrangement

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

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. Positional and directional separation between two positions are of real significance.

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.

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High level Eight position Circular Seating Arrangement 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 Eight position Circular seating arrangement Reasoning Puzzle for SBI PO

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. The eight table positions form the first dimension. The assignments of the other four dimensions are,

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, and
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 will use the following logic table structure on which the problem solving process will be carried out in stages.

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

Help matter: The list of persons and icecream flavors they like are written at the top of the table. When a value from a list is effectively assigned, we cross-out the value thus keeping track of the values left to be assigned. A pair of bidirectional arrows as well will help us to determine right directions. The list of icecream flavors is formed from the condition statements during first quick scan.

Column labels: Eight columns are labelled from 1 to 8 to represent positions on the round table arbitrarily. Actual positions will be determined just after the first person is seated in a position. All subsequent positions persons would occupy will be relative to the first person assignment. This is why you can assign any person to any position as the first person to be seated if you know the name and direction of seating of the person.

Opposite columns: The position numbers are pre-populated in bracket suffix with the opposite position to save time during actual logic processing. For example, first position label 1(5) and fifth position label 5(1) indicate that 1st and 5th positions are opposite to each other.

Note: Mentions of opposite members are valuable for certain assignments.

Row labels: The names of the persons (8), their favorite icecream flavors (8), their facing direction (I/O for IN or OUT) and their gender (M/W for Man or Woman) form four rows of the table.

This is the compact main logic table with 32 empty cells that we have to fill up with the variable values when we are certain of a particular fill.

Temporary logic structures: In addition, 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. Such a second version of logic table will be shown below the main logic table. This will be clear in the course of solving this present puzzle.

Note: Unless absolutely necessary, never create more than two logic table level alternate possibility structures including the main logic table.

Two-degree uncertainty: In a normal case, we can enter a value in a cell of the logic table only when we are certain of its position. Sometimes though we get two values of a variable with certain placement in a cell. For example, we may know that persons B and F occupy positions 2 and 3, but we don't know which position is occupied by whom. This is what we call two-degree uncertainty over two cells and we accept this uncertainty and record it as B/F in position 2 and F/B in position 3. By this, two cells are blocked by two values and a single contradiction against any of these two entries would result in two certain assignments at one go. These are the advantages of a two-degree uncertainty. This two-degree uncertainty in two values over two cells form what we call a Cycle.

Let us start the solution process by selecting the first condition statement and processing it.

Solution to Circular seating arrangement reasoning puzzle for SBI PO: Stage 1: Select first statement with maximum direct certain assignment potential

Choice of the first statement will primarily be determined by the number of persons positionally related with certainty by the statement.

For example, Statement 7. "A who likes Black Currant flavor sits second to the left of D and they face in the same direction." relates two persons A and D by relative positions, but does not create a certain assignment because of absence of facing in or out information. We won't be able to place A and D by Statement 7 anywhere on the empty logic table with certainty as a first placement.

In contrast, Statement 2. "G sits third to the left of E who faces towards the center." positionally relates E and G with certainty because of E facing towards the center. We can then assign these two members separated by two positions to any two positions on the empty table as the first assignment. 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.

In subsequent stages, we will link these just assigned values to build up the filling of the table gradually.

We call this strategy as direct certain assignment first and it is of paramount importance for quick and clean solution of the puzzle.

However, the example satisfying this strategy is a basic one. In its rigorous form, this first assignment strategy guides us to look for not only a statement with direct certain assignment, but actually THE condition statement that has maximum promise for present and future certain assignments.

By the first scan of the conditions we classified this problem as a hard puzzle and so looked for a more effective first statement than the Statement 2 and identified as our first choice,

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

The Statement 9 effectively assigns two persons B and F with two-degree uncertainty to two cells, affects four cells and refers to four persons. It is a highly valuable first choice statement and would be much more effective for faster subsequent assignments than Statement 2.

After placing B/F and F/B in the 2nd and 3rd positions along with "not A, D" information in 1st and 4th positions, we continue to look for reference of A and D that would have positive assignment results and select next another statement with high information content,

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

By elimination it is easy to identify G as the sister of H and place her in the middle of A/D and D/A, another two-degree uncertainty that we always accept.

As positions for A and D have been severely constrained after our first assignment by Statement 9, G in the middle of A/D and D/A could be placed only in position 6 or in position 7. To deal with these two scenarios we create new Possibility 1, a temporary logic table structure below the main logic table. In this new logic table version, all certain assignments of main logic table are duplicated and the second possibility of placements of A and D is recorded.

By itself, every entry in a Possible logic table structure as well as the main logic table is certain within the logic table, but together, the uncertainty is represented in two different placements of A and D.

Strategically, we always accept creation of one extra new Possibility logic table configuration just like the two-degree uncertainty. The advantage is, if we create such an additional partially certain logic table structure, we can continue assignments in both possible logic table configurations with ease. The assurance will always be there that at any point of time a single contradiction would invalidate one of the configurations and would result in a large amount of certain assignments at one go.

Effectively, by this strategy of two possible configurations, the complexity load of logic analysis and chance of resulting confusion is greatly reduced and solution is reached quickly in an assured way.

The logic table after processing the first two statements is shown below.

Solution to circular seating arrangement reasoning puzzle for SBI PO Stage 2: Eliminate second possible logic table configuration by contradiction

In the second stage, with the goal to eliminate one of the two possible configurations (the main logic table and the Possibility 1 configuration are the two possible configurations differing here only in position and direction of A, G and D), we select easily by link search on G,

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

By this statement, the only possible place for E turns out to be position 1 with G at position 6. Thus G cannot be placed at position 7 and Possibility 1 configuration becomes invalid and is crossed off.

The result is shown in Stage 2 logic table below.

Solution to Circular seating arrangement reasoning puzzle for SBI PO Stage 3: Create a second logic table possibility configuration to deal with two degree uncertainty of A and D

The two-cell two-degree uncertainty of A/D and D/A could not be resolved. So, for processing statements referring to A or D, in the third stage we create again a new possible logic configuration Possibility 2 by processing,

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

This made certain assignments by link search easy on both the configurations and three more statements, Statement 3, Statement 10 and Statement 8 are executed one after the other with quick ease.

Let us show you first the result of logic table state and then explain the processing of the statements.

In the first configuration of main logic table A and D look IN and so are placed in positions 5 and 7, whereas in Possibility 2 configuration, A and D look OUT and so are placed in cells 7 and and 5 respectively, just the opposite of the first.

Now selection of statements being easy, first we select by link search on D,

Statement 3."D’s spouse who likes Chocolate flavor sits third to the left of D."

Then by link reference on G,

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

By Statement 3, placement of D's spouse is straightforward as D's facing direction is known in both logic configurations.

Though G's facing direction is not known yet, by Statement 10, G's spouse could also be placed with certainty because of unavailability of two possible placements for G's spouse (as G's facing direction is not known, two possibilities arise for G's spouse out of which one is free and the other is blocked by Chocolate). In the process, facing direction of G is also revealed as O for main table and I for Possibility 2.

The choice of these three statements are quick by simple link search and certain assignments in two logic configurations are also straightforward. This speed could be achieved because of creation of partially certain logic configuration of Possibility 2.

At this point, positions of only two persons C and H out of eight are not known at all in either of the configurations. Persons row becomes the Favorable zone where certain assignments are more likely. So we choose next,

Statement 8. "The immediate neighbors of C like Vanilla and Mulberry flavors."

As expected, by Icecream flavor conflict with Black Currant we could identify C as G's spouse in both the configurations. By exclusion H becomes D's spouse. Achieving enough at this stage, we close the stage and go over to Stage 4.

Solution to Circular seating arrangement reasoning puzzle for SBI PO Stage 4: Eliminate second possible logic configuration by facing direction conflict and achieve certainty

At this point of fairly filled up logic state only, we could identify the statement that eliminates the second Possibility 2 logic configuration by conflict. The statement is,

Statement 1.  "H’s neighbors face in same direction but opposite to that of H."

Let's explain briefly. In main logic table configuration by this statement, H gets facing direction O and person in position 3 gets facing direction I without any problem. In Possibility 2 configuration though the immediate neighbors of H at position 7 (A) and position 1 (E) have opposite facing directions and thus violate the condition of Statement 1. This makes Possibility 2 invalid.

For ease of understanding without processing any more statement we show the result.

Final stage 5 of Solution to Circular seating arrangement reasoning puzzle for SBI PO: Link search, exclusion and a bit of serious elementary logic analysis

Out of total 12 statements four—Statements 4, 5, 6 and 12 are now left to be processed. It is an advanced stage of solution and we don't expect any more difficulty.

To finish off, we observe that the logic table is fairly filled up but the row of gender is nearly empty. So we choose Statement 6 first that mention gender directly for both the persons referred to,

Statement 6."The woman who likes Vanilla flavor sits opposite to the man who likes Red Velvet".

We should mention here that Oppositeness also has special ability to create certain assignment by conflict.

In this case we find first Vanilla candidate E at position 1 has already Black Currant liked by the person in opposite position 5. So the other Vanilla candidate D at position 7 must be the woman and her opposite person at position 3 must be the man liking Red Velvet. By uncertainty cancellation, E at position 1 gets Mulberry flavor.

In addition, D having turned out to be woman, as spouse of a woman H is identified as a man. 

To resolve gender again we select next,

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

Only possibility for the man in this case is A at position 5. The person at position 3 could have been the man concerned if facing direction for this position were O instead of I. So we mark A as a man. In the process C gets facing direction I.

With only two genders left to be determined for positions 1 and 2 and position of B still unknown, next we take up an information rich statement involving B,

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

Out of possible positions 2 and 3, with 3 already liking Red Velvet, B gets position 2 by this statement, and F gets position 3. Furthermore, from the second part of the statement B gets gender W and E gets gender M.

In icecream flavor row, by exclusion G gets Strawberry.

Now we process the last statement to assign the last value of facing direction of B,

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

By this statement B gets facing direction O.

The fully assigned logic table is shown below,

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

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: Circular seating arrangement reasoning puzzle for SBI PO

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.

Note: Option 1 and Option 3 both are partially correct whereas Option 4, a set joining of values of Option 1 and Option 3 fully describes "Who sits second to the left of C" and hence is the right answer to this question. G is a woman and likes Strawberry.

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

Crucial selection of first statement: How to apply the direct certain assignment first strategy in rigorous form to choose the first statement that results in maximum certain assignments and hold maximum information in terms of number of persons referred to and number of cells affected.

Creation of alternate logic structures: Alternate second (and never the third) logic table structures are created at various stages to reduce complex logic analysis load and ease out logic assignments. Assurance was always available that any time with a single contradiction one of the alternatives will be eliminated.

General logic analysis strategies: Achieving maximum amount of certain assignments, higher information content more valuable statement, rigorous form of strategy for selection of first condition to process, Creating possible scenarios, Eliminating uncertainty, working in favorable zones.

Frequently used elementary logic analysis techniques: Direct certain assignment first strategy, Link search technique, Eliminating possible scenarios, Conflict analysis.

Promising positional relations between members: Two-degree uncertainty with two members in two cells, Opposite position members, Cycle formation, adjacent members, neighbors.

Comment

This problem is especially difficult because of large number of 32 cells to be assigned (5 dimensions or variables) with only 12 statements that naturally were mostly compound and complex statements. Crucial to quick solution were right selection of first statement and judicious use of alternate table level logic possibility structures.

To be comfortable with such puzzle solving of any structure and type, there is no alternative other than solving many problems of various types and always analyzing how the puzzle was solved and how the solution can be further improved.

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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

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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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