Solve SBI PO type high level floor stay reasoning puzzle quickly and systematically
The high level SBI PO floor stay reasoning puzzle 1 solved using collapsed column logi table and goal directed logic statement analysis techniques.
For detailed concepts on the fundamental technique 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: Go through the following brief concepts, but before going through the solution of the problem, try to solve the problem in a suitably timed exercise session.
Collapsed column technique adapted to Floor stay Reasoning puzzles
Nature of problem
In a Reasoning Floor stay arrangement problem, a group of people stay in a multi-storied house, usually one person in each floor and no floor vacant, which is a one to one relationship between the set of Persons and the set of Floors. A set of condition statements determine who stays in which floor. This is the simplest form of a problem of this type.
A second level of complexity is introduced often by an additional parameter or characteristic of the persons. This may be a set of professions, a set of hobbies or a set of anything personal. Accordingly, the representation of the logic table changes and the analytical process becomes more complex with an inevitable increase in the number of condition statements to process.
We will solve such a Floor stay Reasoning puzzle of second level difficulty.
Representation of logic table for Reasoning Floor stay problem
Whatever be the complexity level of a Reasoning Floor stay problem, the corresponding collapsed column logic table will have the Floors as the rows, with lowest numbered floor as the bottom row and the highest numbered floor as the top row, other floors in increasing numbers forming the intervening rows sequentially increasing in number from bottom to top. This is an exact replication of the system of floors in a real life multi-storied building. This is the most important characteristic of the logic table representation for this type of problem.
In its simplest form of floor stay problem with only persons to be allotted to floors, only one collapsed column will hold floor assignments of each person. To record intermediate possibilities though we may need to use additional Possibility columns which will be temporarily used till the final allotment.
The upwardly increasing floor numbers is essential for dealing with condition statement like, "Person A stays in a floor just below the floor the person B stays in".
The analysis of the condition statements will be based on the domain knowledge which is common knowledge on floor system of a multi-storied building and so this part is not elaborated further.
As in the problem we are going to solve, each person has an additional characteristic, the logic table will have the same structure with an additional row for each floor. Essentially, there will be one final collapsed column and each floor row a compound row with two cells per column. This is necessary to hold the allotment of a person who stays on a particular floor as well as the additional characteristic of the person, two values for each row column cross-section.
SBI PO type high level Floor stay Reasoning Puzzle : Who stays in which floor and teaches which subject?
Problem description
A building has seven floors numbered one to seven, in such a manner that the ground floor is numbered one, the floor above it numbered two and so on such that the topmost floor is numbered seven. One of the seven professors, namely, A, B, C, D, E, F, and G lives on each floor, but not necessarily in the same order.
Each one of the professors teaches a different subject among the seven subjects, Maths, Psychology, History, Astronomy, Physics, Innovation and Genetics but not necessarily in the same order.
Conditional statements
- Only one person lives between A and the one teaching Maths.
- F lives immediately below the one teaching Innovation.
- The one teaching Innovation lives on an even-numbered floor.
- Only three people live between the ones teaching Maths and Astronomy.
- Only three people live above the floor on which A lives.
- E lives immediately above C.
- E does not teach Astronomy.
- Only two people live between B and the one teaching Genetics.
- The one teaching Genetics lives below the floor on which B lives.
- The one teaching History does not live immediately above B or immediately below B.
- D does not live immediately above or immediately below A.
- G does not teach Psychology.
Questions
Question 1. How many people live between the floors of D and the one teaching Innovation?
- Three
- Two
- One
- More than 4
- Four
Question 2. Who lives on the floor immediately above E?
- The one teaching Innovation
- The one teaching Psychology
- The one teaching Physics
- The one teaching Genetics
- The one teaching History
Question 3. Which of the following subjects does D teach?
- Astronomy
- Psychology
- Genetics
- History
- Maths
Question 4. Four of the following are alike in a certain way and so form a group. Which is the one that does not belong to that group?
- G
- F
- D
- C
- A
Question 5. Which of the following is true with respect to G as per the given information?
- The one who lives immediately below G teaches Innovation
- G lives on the lowermost floor
- G lives on floor numbered 6
- G lives immediately below E
- G teaches Maths
Note: Try to solve the problem yourself before going through the solution.
Solution to the floor stay reasoning puzzle : Problem analysis and representation
There are three sets of objects, the 7 Floors, the 7 Professors staying on each floor, and 7 subjects they teach.
Let us look at the representation first.
In floor stay problems, the logic table representation is very specific. The floors must represent actual physical floors with floor number increasing from bottom to top. As there are 7 floors there will be then 7 row labels with bottom-most row labelled as 1 which represents the floor numbered 1. The topmost floor will be numbered 7 and it will be represented by the topmost row label 7.
As object sets are three in number with unique one to one relation between members of the three sets, the collapsed column will only be 1. The column header label will be, "Professor-Subject". A cell under the single header column and against a specific numbered row will contain the name of the person staying on this floor number as well as the subject being taught by the person. To accommodate two values against each floor, the rows will be compound rows with two rows for each floor.
The final certain allotments of a Professor-Subject pair of values to the seven floors will be accommodated in a single column and seven double cell rows. But while analyzing the logic statements, not always we will be able to allot values to a final column cell with certainty. Instead, we will be able to form more than one possible allotments of a combination of values to one or more than one row in case of partial certainty.
Unless you record such intermediate possible combinations, you won't be able to resolve such an uncertainty by a later statement thereby reaching the final goal much faster.
This gives rise to the need of, what we call intermediate possibility recording. The first column will hold the certain and final assignments and depending upon the complexity of the problem, we will add 1 or more than 1 number of additional Possibility columns to record these interim possible staying combinations.
For our problem we will use two such additional Possibility columns which should be enough for solving this problem we feel. This is the optimal number of temporary possibilities. If it is more than two, it becomes hard and time-taking to analyze and resolve uncertainties quickly. If such a need arises, you should more or less be sure that you are going in the wrong direction.
Thus, the starting logic table will be as below. We will write the lists of names of Professors and Subjects at the top of the table and will go on striking off the name labels as they are assigned to a floor with certainty.
We will start with the following framework of collapsed column logic table.
The seven floors are specified by seven row labels. Each row label represents a compound row consisting of two rows. Against each such compound row, two values for Professor-Subject pair will finally be assigned in the single final assignment column when we are able to make such an assignment with certainty.
Otherwise in case of partial certainty, we will record possible assignment combinations in columns under Possibility 1 and Possibility 2.
Strategic selection of logic statements
For quick systematic solution to any logic puzzle of this type, minimal logic table representation is not enough, it is absolutely necessary also,
To select and execute the logic statements in such a way that at every step the certain assignments to primary object set or potential for such certain assignment is maximized.
In other words, at every step our main objective will be,
To make a certain assignment of a secondary object to a primary object, and if not possible, to create the groundwork for such certain assignments in future as much as possible.
Essentially the selection of the logic statements will not be sequential from beginning to end, but will be determined by suitable strategies that maximize the certainty of assignments to primary object set.
In this way, the suitable logic analysis strategies and the compact column (or row) minimal logic table representation together produce efficient and confident pathway to the final solution.
Let us now solve the problem by analyzing and processing the logic statements.
Solution Step 1
Strategy 1: Certain assignment to a primary object
We will first execute those conditional statements that directly define a certain relation between a secondary object to a primary object, that is, between a person and a specific floor in this case.
In this problem we find no such statement at first. But on closer analysis we find Statement 5: "Only three people live above the floor on which A lives." indirectly says, A can live only on floor number 4. This is an indirect or implicit certain allotment of a person to a floor.
Note: At the start, always look for an explicit and direct certain assignment, if not, search for a statement that implies a certain assignment. In the first step of solving such a problem invariably you should find such a certain allotment. If such a certain allotment is not present at all in the logic statements either explicitly or implicitly, the problem should prove to be unusually complex for attempting in SBI PO or other test environment.
Strategy 2: Link search
After allotting A to floor number 4, we search for a statement that has a reference to A which is already assigned and creates a certain assignment or at most two possible certain assignments of a secondary parameter. This is link search technique and proves to be extremely useful. Essentially, we branch out from the single certain assignment to further certainties, somewhat like a tree.
The Statement 1. "Only one person lives between A and the one teaching Maths." satisfies the criteria and creates two possible allotments of Maths to floor 6 and floor 2. We record these two possibilities in columns Possibility 1 and Possibility 2.
Note that the Statement 11. "D does not live immediately above or immediately below A" also refers to A, but being too general, does not have the potential to create possible certain assignments. Hence it is ignored at this point of time. This statement may become useful at a later stage when the logic table is fairly filled up.
Continuing applying link search technique we look for a statement that refers to subject Maths now. Such a Statement 4. "Only three people live between the ones teaching Maths and Astronomy." enriches Possibility 1 with subject Astronomy in floor 2, and Possibility 2 with subject Astronomy in floor 6. In this action,
Existing possibilities are enriched without increasing number of possibilities.
This is a very important criterion for selecting a statement for processing.
Strategy 3: Analytical certain assignment
At this point we identify a very useful pattern in the cell allotments with respect to the Statement 3. "The one teaching Innovation lives on an even-numbered floor.", which leaves subject Innovation only for floor 4. This is because both the other even numbered floors 6 and 2 have already been blocked by either of Maths or Astronomy. This is the great advantage of recording partially certain possibilities.
Thus it turns out that, A teaches subject Innovation.
Note: This analytically arrived at certain assignment is possible only because the logic table is fairly filled up with certain values. At any stage one should look for such opportunities.
Strategy 2 of link search continued further
Continuing link search technique further, we search for a statement referring to subject Innovation. This results in processing of Statement 2. "F lives immediately below the one teaching Innovation." which allots F to floor 3 with certainty.
After systematic execution of these five statements the logic table looks like,
Solution Step 2
Strategy 4: Processing a group of statements that refer to common elements and form a bonded structure
At this stage of step 2, we are confronted with a difficulty - which statement to process! There is no further link in any of the remaining statements to any of three values already allotted with certainty. This is where we have to be ready to process a single statement or a group of statements that have a common referred element creating a bonded structure that produce an assignment without increasing number of possibilities.
We find such a group in Statement 8. "Only two people live between B and the one teaching Genetics." and Statement 9. "The one teaching Genetics lives below the floor on which B lives." with subject Genetics and professor B being the two common referred elements forming a bonded structure spanning 4 floors with B living above the professor teaching Genetics. These two statements together forces B to floor 6 and Genetics to professor F in floor 3, two certain assignments.
Check this step yourself.
Why B can occupy only floor 6
B and Genetics together form a bonded structure spanning 4 floors with B occupying a floor above the professor teaching Genetics. B couldn't occupy floor 7 because of subject conflict at floor 4. Floor 6 for B and floor 3 for Genetics is a possible assignment. Below floor 6, if B is placed at floor 5 subject conflict arises at floor 2. No other floor below floor 6 is free for B and Genetics separated by two persons.
The four-floor spanning bonded structure is shown on the right of the logic table shown below. In exam hall also you should form such a temporary structure for clear visualization of how it affects the ultimate logic state.
Note: The key is forming a bonded structure between two objects to be assigned. Forming a bonded structure to achieve certain or potential assignments is one of the most important skills for solving complex logic assignment puzzles.
The logic table now looks like,
Solution Step 3: Process a pair of statements that refer to common elements and create an adjacent bonded pair of elements
We continue with the same strategy as in the previous step to identify Statement 6. "E lives immediately above C." and Statement 7. "E does not teach Astronomy.", which together not only forces E to floor 2 and C to floor 1, as E does not teach Astronomy, the second statement also makes the Possibility 1 invalid. This is the crucial state in which we are left with no uncertain Possibility logic structure in the logic table.
The key statement is the Statement 6, that creates an adjacent two-member bonded structure of C-E, with E living above C. As there are no two adjacent floors free for C-E except 1-2, you achieve double certain assignments just by processing Statement 6. Statement 7 then creates conflict with Possibility 1 in subject Astronomy and makes the Possibility 1 invalid.
The two-floor spanning adjacent bonded structure is shown on the right of the logic table in the figure below.
The Possibility 2 column being the only valid one left, it becomes a certainty and its values are to be merged with the Final column. E at floor 2 gets Maths and B at floor 6 gets Astronomy.
We show the logic table state before merging as below,
Solution Final Step 4: Select statements that create certain assignments by elementary logic analysis
This is the final step where only three statements are left. We will select first Statement 11. "D does not live immediately above or immediately below A.", as it definitively forces D to the floor 7, the top floor.
With this assignment professor G, the only one left to be assigned, gets the single unassigned floor 5 with certainty. This is assignment by exclusion, a frequently used technique in solving logic puzzles.
The next Statement 10. "The one teaching History does not live immediately above B or immediately below B." again forces subject History to C in the floor 1, the bottom floor.
At this stage only two subjects Physics and Psychology are left to be assigned. The Statement 12. G does not teach Psychology." decides subject Physics for G and Psychology for D.
You will notice that at this final stage the assignments could be done easily using elementary logic analysis. This usually is the case because of the fairly filled up logic table with practically no room for many uncertain possibilities at this final stage. The more you assign the cells the less becomes the uncertainty level of the logic table.
The logic table is now fully assigned and shown below.
The two possibility columns in the above figure have no more use. We have shown these just for symmetry between all the figures.
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. How many people live between the floors of D and the one teaching Innovation?
Answer 1. Option 2: Two.
Question 2. Who lives on the floor immediately above E?
Answer 2. Option 4: The one teaching Genetics.
Question 3. Which of the following subjects does D teach?
Answer 3. Option 2: Psychology.
Question 4. Four of the following are alike in a certain way and so form a group. Which is the one that does not belong to that group?
Analysis: As among the five choice values of Professors G, F, D, C, A, all the four of G, F, D, C live on odd numbered floors they form a group with only A living on an even numbered floor 4. So A does not belong to this group. You need to take special care in answering this type of question
Answer 4. Option 5: A.
Question 5. Which of the following is true with respect to G as per the given information?
Answer 5. Option 1: The one who lives immediately below G teaches Innovation.
All the other options are false.
Recommendation
Without solving a sufficient number of such logic assignment problems during timed practice sessions one may not gain enough confidence and ability to solve a tricky logic puzzle or logic analysis question in an important competitive test.
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.
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
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