SBI PO type high level reasoning puzzle solved in a few confident steps 3

Submitted by Atanu Chaudhuri on Sat, 08/04/2017 - 13:41

Three object set reasoning puzzle similar to linear sitting arrangement is not so simple

This is the third session on solving a SBI PO type high level reasoning puzzle in a few easy and confident steps without confusion. Minimal form of logic table along with strategic selection of logic conditions for execution enable quick solution without confusion for this 3 object set assignment problem with a twist.

The twist is in the structure of the problem. Instead of straightforward assignment between object sets, an additional attribute of 'before-after' makes the problem more complex. The complexity is partly reflected by the larger number of logic statements which is 11.

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

How to solve SBI PO level logic puzzles in a few simple steps 1

How to solve SBI PO level logic puzzles in a few simple steps 2

How to solve SBI PO level family relation problems in a few simple steps 3

How to solve SBI PO level floor stay Reasoning Puzzle in a few confident steps 4

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

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

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

SBI PO type high level Reasoning Puzzle equivalent to a linear sitting arrangement puzzle: Who is from which city and attended seminar in which month?

Problem description

Each of seven persons, Sonali, Uma, Tejinder, Vinay, Samir, Gauri and Rupchand attended a seminar on seven different months of the same year namely January, February, March, June, August, October, and December but not necessarily in the same order. Each of them also lives in a different city namely Patna, Kolkata, Ranchi, Chennai, Pune, New Delhi and Indore but not necessarily in the same order.

Conditional statements

Tejinder has a seminar in a month which has less than 31 days.
Only two persons have a seminar in months between Tejinder and Vinay.
The one who lives in Patna has a seminar in a month immediately before Samir.
Only one person has a seminar in a month before the one who lives in Ranchi.
Uma has a seminar immediately after the one who lives in Ranchi.
Only three persons have a seminar between Uma and the one who lives in Pune.
Samir lives neither in Pune nor in Ranchi.
Sonali has a seminar immediately before Samir.
Rupchand lives in Indore.
The one who lives in Kolkata has a seminar in the month which has less than 31 days.
The one who has a seminar in March does not live in Chennai.

Questions

Question 1. Who attended a seminar just before Uma?

Tejinder
Vinay
Gauri
Samir
Rupchand

Question 2. Who are the two that attended their seminars just before and just after Sonali?

Uma-Vinay
Gauri-Uma
Vinay-Rupchand
Samir-Tejinder
Tejinder-Samir

Question 3. In which month did Rupchand attend the seminar?

February
January
June
October
December

Question 4. Who attended their seminars in months with less than 31 days?

Gauri, Tejinder
Tejinder, Samir
Vinay, Tejinder
Tejinder, Uma
None of the above

Question 5. Which is the odd pair among the following five pairs of persons?

Uma-Tejinder
Vinay-Rupchand
Samir-Gauri
Rupchand-Tejinder
Vinay-Sonali

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

Solution to the SBI PO type high level reasoning puzzle equivalent to a linear sitting arrangement puzzle: Problem analysis and representation

Though the number of object sets is 3, viz. the persons, the months and the cities, because of larger number of members in each set of objects, which is 7 (compared to 6) and an additional element of Direction ('before-after) between the primary objects, viz. the months, the complexity of the problem is more compared to the previous problem we solved. Consequently we find the number of statements for full assignment is also more, that is 11. We are comparing the figures with the 4 object set each with 6 members puzzle we solved in our previous session with only 7 logic statements.

Let us look at the representation first.

Logic table Representation

Because of the 'before-after' direction attribute in months set, it is convenient to place the months as column labels in horizontal direction. Thus this problem is similar to linear sitting arrangement puzzle in which 'left-right' direction in logic statement is a similar necessary attribute. The months become the natural primary object set to which the persons and the corresponding cities will have to be assigned by analyzing the 11 logic statements.

So the persons and the cities form the two rows, members of which are to be assigned to the months, and in the process, to each other (as this is an one to one unique assignment problem).

Finding an additional attribute of 'less than 31 days' we decide to create for convenience a third row with fixed assigned values of '< 31 days' to months February and June, the only two months with days less than 31.

We use the three object lists at the top of the table (we could have used lists only for persons and cities also) to keep track of assignments already made and which member is yet to be assigned. By striking off the already assigned member of a list we keep track of the members yet to be assigned.

From our experience in collapsing columns (and rows) of logic table to the only one finally assigned column (or row), we decide to use the complete column as well as row collapsed minimal form of logic table as below.

SBI PO type high level reasoning puzzle solved in a few confident steps 3-1

We have selected seven columns one each for one month and two rows for Persons and Cities of residence. There are no superfluous cells in this minimal logic table (the Days row is a fixed value row which is created for convenience. Its empty cells provide useful information but are not for assignment consideration). The two main rows will hold only the final assignments. If at all we need to record any uncertain assignments, we will record the condition in its raw form, but only if it can be recorded against a column, that is against a particular month.

Essentially the whole challenge of solving the problem quickly without confusion is shifted to the strategic selection of efficient sequence of condition statements for execution. This approach should not only lead to the quickest solution, but also will test the core skill of logic analysis of the problem solver.

Let us now solve the problem by analyzing and processing the logic statements. As usual our objective will be to make full assignment and fill up the Final columns exhaustively and in as few steps as possible.

Solution Stage 1

Strategy 1: Identify direct assignment to a column member with maximum number of certain assignments: Direct assignment first strategy

We will first execute only those conditional statements that directly assign any of the row members to a column header member and have most number of such assignments.

If there are more than one such statement, the single statement with maximum number of certain direct assignment to a column header value will be chosen first.

Furthermore, such a direct certain assignment may be explicit and easy to find or it may need to be deduced and implicit (hidden) in nature.

Without such a direct assignment further progress would have been difficult. On the other hand, with one direct assignment, a few cells are filled up, and we will select suitable statements next, using these filled up certain assignments. These certain assignments will help further efficient progress immensely.

We find no single statement that makes a direct certain assignment of any row value to any month value. Consequently we look for hidden or implicit certain assignment and find the desired statement in "Statement 4: Only one person has a seminar in a month before the one who lives in Ranchi."

As there is only one month before the month corresponding to Ranchi, that single month must be January and Ranchi must be corresponding to February. This is an example of logical deduction.

Strategy 2: Looking for useful reference to the filled up cell values: Link search technique

As there is no more certain assignments, we start looking for a statement linked or referring to Ranchi, the already assigned value. This is execution of Strategy 2, the link search technique.

Thus by link search technique we use "Statement 5: Uma has a seminar immediately after the one who lives in Ranchi." to place Uma against month March with certainty.

Note: The reason to search for links to already obtained certain knowledge instead of other types of conditional statements lie on the basic mechanism of building of rich knowledge by linking isolated pieces of facts or concepts,

A single body of knowledge comprising of a number of interlinked pieces of concepts is essentially more powerful and effective than many pieces of isolated facts or concepts.

Again we fall back upon Strategy 2 of link search technique, but now we search for statements that refer to Uma.

Analyzing such a "Statement 6: Only three persons have a seminar between Uma and the one who lives in Pune.", we deduce that by the nature of the statement, Pune cannot be assigned to a month before March (there are not enough number of months before March). So Pune automatically gets a certain assignment against month December.

Note: Logical deduction is an essential activity in executing a strategy.

It is time now to process more than one statement together according to Strategy 4.

Strategy 4: Objective of finding a direct assignment that results in certain assignments by processing more than one statement: Statement group execution

The "Statement 1: Tejinder has a seminar in a month which has less than 31 days." together with "Statement 2: Only two persons have a seminar in months between Tejinder and Vinay." assign Tejinder against the middle month of June with certainty and possible assignment of Vinay in two end months of January and December. We record this uncertain information with a question mark against Vinay in both the cells.

Note: It is important to record this information with only two degree of uncertainty (Vinay possible in only two cells), because this not only completes processing of the corresponding statement but creates potential for future certain assignments by conflict of values easily. In case of conflict in one possibility the other possibility becomes certain. This is why we go for uncertainties of maximum two degrees and not more.

After systematic execution of these five statements in Stage I, the logic table looks like,

SBI PO type high level reasoning puzzle solved in a few confident steps 3-2

Solution Stage 2

Now with the fairly populated logic table we adopt the Strategy 5, that is, looking for horizontally linked or bonded structures.

Strategy 5: looking for horizontally (vertically linked for floor puzzles) bonded or linked member structures

The reason for adopting this strategy at this point lies in the fact that with rows partly populated, such a bonded structure gets a constrained or limited number of possible assignments. More often than not, these constraints or conflicts force one or more than one certain assignment.

"Statement 8: Sonali has a seminar immediately before Samir." forms such a bonded two person structure of 'Sonali-Samir' with Sonali before Samir and the two adjacent to each other.

Now we look for a link with Sonali or Samir as per Strategy 2 and find it in "Statement 7: Samir lives neither in Pune nor in Ranchi." The conflicts in Ranchi and Pune puts Sonali-Samir pair against August-October month pair with certainty.

We can also think of the step as executing Strategy 4.

Continuing link search we find that by "Statement 3: The one who lives in Patna has a seminar in a month immediately before Samir." Sonali gets Patna.

Strategy 6: looking for conflicts in assigned member values: Principle of conflict

Lastly at this point in "Statement 9: Rupchand lives in Indore" we detect the possibility of placing Rupchand-Indore pair in January with certainty because of conflicts in either city or unavailibility of person cells.

With this assignment at last Vinay gets December assignment with certainty. Out of two possible placements for Vinay one is eliminated making the other a certainty. By principle of exclusion, Gauri then gets assigned to February.

Both principle of conflict and principle of exclusion are at work in these steps.

This is elementary logic analysis.

Check these steps yourself.

The logic table now looks like,

SBI PO type high level reasoning puzzle solved in a few confident steps 3-3

Solution Stage 3

At this point, as the logic table is well filled up, by executing the last two statements in suitable sequence the rest of the empty cells could easily be filled up.

By the "Statement 10: The one who lives in Kolkata has a seminar in the month which has less than 31 days.", Tejinder gets Kolkata, as the other less than 31 days month of February has already been taken up by Gauri. This is principle of exclusion at work.

Lastly, "Statement 11: The one who has a seminar in March does not live in Chennai." finally decides the city of New Delhi for March and Uma pair and so by exclusion Chennai is assigned to October-Samir pair. This is first logic deduction and then exclusion.

It is not so difficult, isn't it?

The final logic table state is as below,

SBI PO type high level reasoning puzzle solved in a few confident steps 3-4

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 attended a seminar just before Uma?

Answer 1. Option 3: Gauri.

Question 2. Who are the two that attended their seminars just before and just after Sonali?

Answer 2. Option 5: Tejinder-Samir.

Question 3. In which month did Rupchand attend the seminar?

Answer 3. Option 2: January.

Question 4. Who attended their seminars in months with less than 31 days?

Answer 4. Option 1: Gauri, Tejinder.

Question 5. Which is the odd pair among the following five pairs of persons?

Answer 5. Option 1: Uma-Tejinder, they are in adjacent months, with all the other four in non-adjacent months.

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.

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.