5 Variable Tough Reasoning Puzzle for SBI PO Solved in Easy Steps

Submitted by Atanu Chaudhuri on Sun, 16/04/2017 - 20:57

A five variable reasoning puzzle for SBI PO to test your assignment logic analysis skills

The 5 variable reasoning puzzle for SBI PO is tough. But with systematic logic analysis, the puzzle is solved in easy and confident steps without confusion.

First the reasoning puzzle for SBI PO is described and then it is solved in three strategic stages.

For detailed concepts on the fundamental techniques and strategies used in solving this type of logic puzzles you should read 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.

Tough Reasoning Puzzle for SBI PO with five variables: Who is of which gender, has which hobby, likes which friend of what profession?

Problem description

There are five Managers M1, M2, M3, M4 and M5. Each has a different hobby among Philately, Shopping, Writing, Trekking and Sudoku but not necessarily in the same order. Each Manager has friendship with a person among S1, S2, S3, S4 and S5. Each such friend has a different profession among Chef, Architect, Painter, Surgeon and Photographer but not necessarily in the same order.

Conditional statements

Among Managers, there are only three females, the one who has friendship with S3, the one whose hobby is Philately and the one who has friendship with the person who is a Surgeon.
The person who is an Architect has no friendship with the person whose hobby is Writing.
The female whose hobby is Shopping has friendship with the person who is Painter.
M2’s hobby is Trekking.
S4 is neither an Architect nor a Chef.
The Manager who has friendship with S5 is a female but she is not M4.
M5’s hobby is shopping and is not a male.
M1 and M3 are not females.
M1’s hobby is Sudoku and is friend neither with S5 nor with Architect.
S5 is not Painter.
The one who is a Chef has no friendship with M4.
S2 is a Chef and he has no friendship with M1.

Questions

Question 1. Who is a photographer?

Question 2. Who is the friend of a surgeon?

Question 3. Which female has Philately as hobby?

Question 4. What is the profession of friend of M3?

Painter
Architect
Photographer
Chef
None of the above

Question 5. Which of the following combinations is correct?

S4-Photographer-M3
S2-Chef-M2
S1-Architect-M4
S1-Architect-M3
S4-Photographer-M2

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

Solution to Tough Reasoning Puzzle for SBI PO with five variables: Initial stage: Problem analysis and representation

At first number of object sets seems to be 4 in number, the 5 managers, their 5 hobbies, their 5 friends and 5 professions of the friends. Till this point, the problem is a purely one to one assignment logic analysis problem,

On a second look though, the fifth object set of 2 genders of the managers comes to light thus increasing the number of objects to be assigned to each other to 5, the gender to manager relationship being one to many.

A general property of the assignment logic analysis puzzles of this type is,

Complexity of puzzle problem increases significantly with each single increase in number of assignment object sets after 4 such object sets.

An excellent example of such a puzzle problem is what is popularly known as the Einstein's whose fish puzzle that has six object sets of 5 members each to be assigned among each other one to one. If interested you may refer to the methodological solution of Einstein's whose fish puzzle and try to solve it before going through the solution as a way of sharpening your assignment logic analysis skills.

Our present problem also has 5 members in each of the four main object sets. But the gender set has only two values. Assignment of these values should be easy and once fully assigned, these values should help in other assignments. This reduces the problem complexity, even though the object sets are 5 in number.

Scanning through the 12 logic statements, which is a large number, we decided that the first objective should be to assign gender fully and with the help of gender assign further values. This is the first general strategy formed.

One of the minor difficulties faced was in choosing which set of persons should be the primary object set forming the column labels.

It was decided that the Managers will form the primary object set, as it has two property object sets in Hobbies and Genders, whereas Friends has only one such property in Professions. The difficulty was felt particularly because of the presence of two Persons object sets each with their own properties.

It is generally true that,

Wrong choice of primary object set may jeopardize the chances of confident solution significantly.

The following is the logic table representation we will work on.

5 Variable Tough Reasoning Puzzle for SBI PO Solved 5: logic table

Hobby and Gender were placed as the first two rows as these are the properties of the primary object set of Managers. The Friends and their Professions went as the lower half rows of the logic table.

Members of five object sets are listed at the top of the logic table to keep track of the assigned member belonging the four secondary objects sets by striking off the assigned member.

Solution to Tough Reasoning Puzzle for SBI PO with five variables Stage 1: Direct assignment first and link search strategy: Maximum assignment with certainty

This is maximum certainty assignment strategy followed as an overriding strategy. At the beginning, action as per this strategy should be more beneficial for this type of assignment puzzles than any other.

To achieve the goal of maximum amount of certain assignment without increasing uncertainty the very first strategy that we use is the direct assignment first strategy. We look for statements that make direct and certain assignments to the primary object set (in this case to the column members). The statement that makes most number of certain assignments without any uncertain clauses is chosen.

During subsequent steps, by link search technique we link other statements that refer to any of the already assigned values and increase certain assignments.

Only after populating the logic table to a fair degree, we take up the more complex statements that contain negative uncertain clauses.

For this problem, we will first execute the statement that make direct certain assignment. Statement 7. "M5’s hobby is shopping and is not a male." is chosen first as it makes two assignments as well as linked to the Statement 3. "The female whose hobby is Shopping has friendship with the person who is Painter." without introducing any uncertainty. Thus with these two statements we get an assignment of three values for M5 column, a fairy satisfactory result.

Link search technique of selecting statements with common referenced elements is one of the most useful techniques for solving these problems.

Next we choose Statement 4. "M2’s hobby is Trekking." as it makes one direct certain assignment without introducing any uncertainty. This statement is preferred over Statement 9. "M1’s hobby is Sudoku and is friend neither with S5 nor with Architect." as the statement 9 introduces a fair amount of uncertainty with negative conditional clauses though it has one certain assignment.

This approach is the Maximum certain assignment without increasing uncertainty. When the logic table is fairy filled up with certain assigned values, the statements with uncertainties help to create certain assignments, but not in the early stages with sparsely filled logic table.

After these initial more effective and necessary steps, we focus our attention now to fully assign the Gender row quickly by selecting the Statement 8. "M1 and M3 are not females." that assigns two Male values to M1 and M3.

The logic table after this first stage is as below,

5 Variable Tough Reasoning Puzzle for SBI PO Solved 5: Stage 1

Solution to Tough Reasoning Puzzle for SBI PO with five variables Stage 2: Strategy 2: Assigning the small member Gender set fully

With the objective of assigning the two member Gender set fully we select Statement 1. "Among Managers, there are only three females, the one who has friendship with S3, the one whose hobby is Philately and the one who has friendship with the person who is a Surgeon." because first it indicates the number of females as 3 so that immediately M2 and M4 can also be assigned Female value.

Furthermore, as the three females are three distinct Managers, M4 can be assigned hobby as Philately with certainty (because other two females M2 and M5 have already assigned hobbies. Next, by the same reasoning Surgeon friend is assigned to M2 as M5 already has Painter friend and M4 has already been treated by this statement. So to complete the effect of this useful statement, S3 is assigned as the friend of left out M5.

Next we choose the earlier ignored Statement 9. "M1’s hobby is Sudoku and is friend neither with S5 nor with Architect." because it makes a certain assignment Sudoku as hobby of M1 and consequently helps another certain assignment of hobby Writing to M3 by principle of exclusion (this is the only place left with only one value left to be assigned).

The two uncertainties are noted as, "not S5" and "not Architect" in corresponding cells.

But we could detect Statement 2. "The person who is an Architect has no friendship with the person whose hobby is Writing." which could assign Architect friend to M4 as, M1 and M3 are negated from the 3 possible members.

Taking up the strategy of two degree allowable uncertainty, the professions of two friends for M1 and M3 are filled with two values, "Chef/Photographer".

Check these steps yourself.

The logic table now looks like,

5 Variable Tough Reasoning Puzzle for SBI PO Solved 5: Stage 2

Solution to Tough Reasoning Puzzle for SBI PO with five variables Stage 3: Strategy 3: Resolving uncertainties with link search and conflict

At the very beginning of this stage we could identify an opportunity to resolve the two degree uncertainty of "Chef/Photographer" by the Statement 12. "S2 is a Chef and he has no friendship with M1.", as it refers to Chef and negates friendship with M1, thus leaving M3 as the certain assignment for profession Chef. By cancellation of Chef from its two possible values, M1 gets profession of friend as Photographer. Additionally M3 gets friend S2.

This uncertainty cancellation, resulting in a certainty.

Try to absorb the advantage of adopting two degree uncertainty strategy.

Now is the time to fill up the friend identities.

We select next the Statement 6. "The Manager who has friendship with S5 is a female but she is not M4." as it refers to two females M2 and M4 by exclusion, and negates M4, thus leaving S5 for M2.

Lastly Statement 5. "S4 is neither an Architect nor a Chef." finalizes S4 for M1 and by exclusion M4 gets friend S1.

Check this step yourself.

This is a good example of elementary logic processing along with strategic selection of statements for execution.

Observe that the Statement 10. "S5 is not Painter." and Statement 11. "The one who is a Chef has no friendship with M4." both have not been used at all. These have become superfluous and redundant.

Nevertheless we can use these to see whether the conditions conflict with our fully assigned logic table or not. This is, verifying a small part of our assignments.

Verification of final logic table

This produces a new idea of verification of the fully assigned logic table by the problem description and and logic conditions, especially when you are not under time pressure. This is a valuable practice and improves the confidence level immensely.

While verifying, move right from the first statement and sequentially down to the end.

The final logic table state is as below,

5 Variable Tough Reasoning Puzzle for SBI PO Solved 5: Stage 3 final

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 is a photographer?

Answer 1. Option 3: S4.

Question 2. Who is the friend of a surgeon?

Answer 2. Option 1: M2.

Question 3. Which female has Philately as hobby?

Answer 3. Option 2: M4

Question 4. What is the profession of friend of M3?

Answer 4. Option 4: Chef.

Question 5. Which of the following combinations is correct?

Answer 5. Option 3: S1-Architect-M4.

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.