## SBI PO level Reasoning floor stay problems can also be solved quickly by collapsed column technique

We have discussed logic analysis in our earlier sessions onĀ * Simple logic analysis* ,

*and efficient method of collapsed column logic analysis technique for solving SBI PO or higher level logic puzzles in our previous sessions on*

**Complex logic analysis***,*

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

**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.**In this session * we will further expand the scope of the powerful method* through solving a

*with characteristic ease.*

**SBI PO level Reasoning problem on Floor stay arrangement**Before going through this session, you are urged to go through the above-mentioned **first, second and third session on efficient solution process for logic puzzles.**

The following section repeats the basic theory behind the Collapsed column technique in solving Assignment logic analysis problems. If you are already aware of the background concepts, you may skip this section.

### Assignment logic analysis using Collapsed column logic analysis technique can be applied to a number of Reasoning problem types

In * Assignment logic analysis problems* there is a set of objects that are to be assigned (or mapped) to a second set of objects determined by a set of logic statements or conditions.

The objects that are to be assigned belong to the to-be-assigned object set (TBA object set) and the objects to which the to-be-assigned objects are to be assigned belong to the to-be-assigned-to object set (or TBAT object set). * In case of one-to-one unique assignment* between two object sets, any of the two object sets are interchangeable with the other with respect to assignment as an assignment between two objects is a mutual two directional operation.

In the simplest form of assignment logic analysis problem, one set of objects are to be assigned to a second set of objects according to a third set of given conditions. The conventional method to solve this form of problems is to represent the values of the two object sets, one as rows and the second as columns. **This representation is the simplest form of 2 dimensional logic table.**

The cell values represent assignment between the members of the two sets. For example one set may be husbands and the second wives; problem will be to determine who is married to whom according to a set of conditions. The names of husbands may form row labels and names of wives column labels. Cross section of a row and column will represent marital status of the pair involved.

Commonly we encounter logic analysis problems of assignment type in * logic puzzles* which occasionally seem to be quite confusing. We have already used the efficient technique of collapsed logic table columns in solving logic puzzles and family relation problems in our earlier sessions.

In this session, we will apply the * same technique with a minor adaptation* to solve a different category of Reasoning problems, namely

*problems. In future sessions we will show how the same method can be applied for efficient solution of*

**Reasoning Floor stay arrangement***as well.*

**Sitting arrangement type of Reasoning problems**Use of same concept and similar method in solving varieties of Reasoning problems eases the overall problem of solving a large portion of difficult reasoning problems considerably.

The subcategory of Floor stay arrangement problems essentially fall under the general category of Assignment logic analysis problems, where **a set of persons** *stay in a set of floors* and the * persons may have one or more than one set of characteristics*, such as, profession, age, liking of food, and so on.

Usually all the sets have same number of members so that the assignments are of one to one type. With increase in number of members in each set (such as more number of floors and more number of persons) or increase in numbers of sets itself, the complexity of the problems of this type increases. Occasionally though we encounter more complex problems where * complexity lie* in

*between the member sets.*

**one to many relationship**The assignments are to be determined for all such problems by a given set of statements or logic conditions.

The following section explains the theory behind the Stages in solving Reasoning logic analysis problems of assignment type.

### Stages in solving Reasoning logic analysis problems

#### Problem structure analysis and representation

One of the most important stages in solving reasoning logic analysis problems of any type is the * first stage* of

*Unless such a problem is represented in appropriate efficient form, attempt to solve the problem in any which way most possibly ends up in confusion.*

**Problem structure analysis and representation.**For example, in our earlier logic puzzle solution we have identified its nature as an * assignment type logic puzzle problem* and used the final collapsed column logic table of the form,

This forms an example of **one to many type of logic assignment.**

For * floor stay arrangement problems*, the

**problem representation will take a different form.**#### Sequence of logic statement execution - Strategy

In the * second stage, we Analyse logic statements in conjunction with the problem state* to determine the

**sequence of executing or processing the logic statements.**Any logic problem will have a prime component in the form of a set of logic or condition statements. * In second stage we determine the efficient sequence of executing the conditional statements.* On an appropriate problem representation

**if we can apply an efficient sequence of execution of logic conditions, often the problem is solved much faster.**#### Individual logic statement analysis

In the * third repetitive stage we actually carry out analysis and execution of one or more than one logic statement at each step.* This is the last level and

*With proper execution of the individual logic statements coupled with proper sequencing or selection of logic statements for execution, the problem logic table can be simplified greatly at a single step.*

**forms the core of elementary logic analysis.**#### Importance of domain knowledge at the third stage of individual logic analysis

At this third stage, the * clarity in domain knowledge plays a critical role.* For example, in the process of solving a reasoning problem on family relations,

**you must be very clear about the commonly accepted form of relations between various members of a common family.**On the other hand, * for a floor stay arrangement problem*, you need to be

*"floor above" or "floor below", and be able to*

**clear about the meaning of relations***"one floor above" and "floor above". The second statement may refer to a floor above the floor referred to*

**differentiate****between the relations,***, whereas in the first instance, target floor is just above the the floor referred to. These concepts belong to the*

**by any number of floors***. Without clear understanding of the meaning or concepts of the statements referring to this domain, solving a complex floor stay arrangement problem may not be easy.*

**domain of floor stay arrangement**

### Collapsed column technique adapted to Floor stay arrangement logic problems

#### 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 problem of this type.**

The **first problem we will solve is of this level**, and we will use the solution to demonstrate the process of solution in fine detail.

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, the analytical process and the number of condition statements will also increase.

You may refer to such a * solved problem of this higher complexity level* in our session on

**SBI PO level Solution set 1 on Reasoning floor stay problem.**#### 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.

This form of logic table representation 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. We will get the feel of the nature of such condition statements and the analysis through the solution process of the following example problem on the topic.

### Problem example 1: Reasoning Floor stay arrangement problem 1: Who stays in which floor?

#### Problem description

A building has eight floors numbered one to eight, 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 eight. One of the eight persons, namely, A, B, C, D, E, F, G and H lives on each floor.

#### Conditional statements

- E lives above F.
- Only two persons live between the floors of C and G.
- H lives on the floor immediately above the floor of B.
- Only one person lives between the floors of E and F.
- C lives on third numbered floor.
- Only one person lives between the floors of C and D.
- D lives on a floor below the floor of E.

#### Questions

**Question 1.** Who among the following lives on the topmost floor?

- C
- B
- H
- G
- E

**Question 2.** Four of the following five are alike in a certain way and hence they form a group. Which one of the following does not belong to that group?

- G
- C
- A
- D
- B

**Question 3.** Who among the following lives on the fifth numbered floor?

- A
- D
- B
- H
- G

**Question 4.** How many persons live between the floors of B and F?

- 1
- 2
- 4
- 5
- 3

**Question 5.** Who among the following lives exactly between the floors of C and D?

- E
- F
- A
- G
- H

#### Problem example 1: Solution to the floor stay reasoning problem 1: Problem analysis and representation

There are only two sets of objects, the 8 Floors, and the 8 Persons staying on each floor. Inherently the problem should be simple.

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 8 floors there will be then 8 row labels with bottom-most row labelled as 1 which represents the floor numbered 1. The topmost floor will be numbered 8 and it will be represented by the topmost row label 8.*

* As object sets are only two in number, the collapsed column will only be 1*. The column header label will be, "Person". 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.

Till this point on the structure is simple, *an eight row single column collapsed table.*

But * a floor arrangement problem may hide its complexity in the staying statements that determine who stays in which floor*.

Quite often while analyzing a specific statement or a group of statements at one stage, * you may not be able to specify a person against a floor with certainty.* Instead, you may have to

*Unless you record such a possibility, you won't be able to resolve such an uncertainty by a later statement thereby reaching the final goal much faster.*

**specify only two or more possible combinations of staying arrangements of persons.**For any efficient solution of this type of problem, * forming, recording and later resolution of possible combinations* are essential activities. This falls under the general skill category of

**Pattern Identification and Use. Sudoku game play is rich with this type of pattern identification challenges.**This gives rise to the need of, what we call * intermediate possibility recording.* The

*and depending upon the complexity of the problem, we will add 1 or more than 1 number of*

**first column will hold the certain and final assignments***to*

**additional Possibility columns***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. In any case, if we need we can increase the number of Possibility columns any time while solving the problem.

Thus, the starting logic table will be as below. We will write the list of names of persons at the top of the table and will go on **striking off the name labels as they are assigned to a floor with certainty.**

This basically is the logic table representation that we will use for solving this floor problem. As explained earlier, the eight floors are specified by eight row labels against each of which the person staying in the floor will be marked in the first column, when such an assignment we can make with certainty. Otherwise we will record **possible assignment combinations in column Possibility 1 and Possibility 2.**

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 column exhaustively.

#### Solution Strategy 1 - Step 1

*W** e will first execute those conditional statements that directly define a relation between two members of the two object sets, that is, between a person and a specific floor*. In this problem, there is only one such

**Statement 5**:

*"C lives on third numbered floor."*So we will directly assign C against floor 3 and go over to next step. The logic table looks like,

**Solution Strategy 2 - Step 2**

The specialty of this problem is, * at this early stage of step 2, we are confronted with a difficulty* - which statement to process! This is the hallmark of a good logic analysis problem even in a two object set assignment problem.

The * key to find the next statement lies* in

*. By a quick scan through*

**strategy 2 of analyzing the statements that refer to the certainly assigned C, as well as helps in another certain assignment***(this is where your agile logic analysis skill will come into play)*the remaining statements, we find that

**Statement 2:**

*"Only two persons live between the floors of C and G."*is the only such statement.

It refers to C and G in such a way that **G must be assigned to three floors above C**, that is, * on Floor 6*.

**G cannot be assigned three floors below C as C is on Floor 3**. There is no zero numbered floor here. This is a typical example of how individual floor assignments are resolved **based on the special characteristics of the floor system.**

The logic table now looks like,

**Solution Strategy 3 - Step 3**

At this stage there is no other avenue open than to **analyze a few statements together. Basically this is the third strategy at this juncture.**

**The objective will be to form a combination of two or more persons living at corresponding number of floors, separated by a certain number of floors, and preferably specified by who lives above or below whom. **

This is called a **bonded structure.**

**We won't be able to assign the persons involved in the bond against specific floors**, but after analyzing against the present logic table, we should able to specify *two or more possible floor assignments to the bonded person structure.* We will record **each floor assignment combination of the bonded structure against a fresh possibility column.**

Combinations of each of these possibilities will have to taken together with the already certain assignments to form a complete possible state.

Let us explain this rather theoretical logic exercise with actual logic statement execution.

**Statement 1:** *"E lives above F."* and **Statement 4:** *"Only one person lives between the floors of E and F."* are the first two candidates to form such a * bonded person-floor component* where E lives above F with exactly one floor between them. It creates a

**three floor (element) bond.**

* Testing the placement of three element bond* of E and F (three floors and two persons E and F, with one floor between them) against fixed assigned C at floor 3 and G at floor 6, we find easily that the possibilities are limited to only two,

**Possibility 1:**

**E on floor 7 and F on floor 5;**and

**Possibility 2: E on floor 4 and F on floor 2**. There is no other possible combination.

We record these two possibilities **in two separate additional possibility columns.** Each E-F combination of a possibility has to be read with the already assigned Final column combination. So, **Possibility 1 will read as**,

**Possibility 1:** C on floor 3, F in floor 5, G in floor 6 and E in floor 7.

Similarly Possibility 2 is to be read as,

**Possibility 2:** F in floor 2, C on floor 3, E on floor 4 and G on floor 6.

**You need to carefully verify this step yourself.**

The logic table state is shown below with two possibility columns used.

**Solution Strategy 4 - Step 4**

Out of the three statements left, we find **Statement 6:** *"Only one person lives between the floors of C and D."* cannot give us any useful bond structure or specific assignment as D is yet to be assigned.

The **Statement 7:** *"D lives on a floor below the floor of E."* could have been processed enriching each of the possibilities, but we find the **Statement 3:** *"H lives on the floor immediately above the floor of B."* creates * a strong two element bond containing more information* which we could place

*and*

**on top two floors for possibility 2***. This enriches each combination of the possibilities*

**bottom two floors for possibility 1***.*

**without increasing the number of possible combinations**This is the logic statement * that addresses maximum number of additional assignments without increasing the number of possibilities.* This characteristic is at the core of the Strategy 4 at any stage.

*Mark the second part of the characteristic, the number of possible combinations must not be increased, if any other option is available. In other words,*

While processing logic statements, only those statements need to be executed that keep number of possible combinations (or number of possibility columns) to a minimum.

Check out this step yourself.

The logic table condition is as below,

**Solution Strategy 5 - Step 5**

Only two statements are left now. As D is yet to be assigned a possible floor, we won't execute **Statement 6**: *"Only one person lives between the floors of C and D.", *but process the **Statement 7:** *"D lives on a floor below the floor of E."* as **D can be placed only on** **floor 4 for Possibility 1**, and **floor 1 for Possibility 2**. This enriches the two possibilities without increasing the number of possible combination. This **satisfies the criteria of Strategy 4.**

The corresponding logic table is as below,

#### Solution Stategy 6 - Step 6 - Execution of last statement and final choice between the two possible combinations

When we test the last **Statement 6:** *"Only one person lives between the floors of C and D."*, against the Possibility 1 combination, * this possibility turns out to be invalid*, as here the floors of

*.*

**C and D are adjacent to each other that violates the Statement 6 condition of one person between C and D**On the other hand, for Possibility 2, only F lives between C and D and **so it satisfies the Statement 6 condition perfectly.**

We strike out the Possibility 1 combination and merge the combination of Possibility 2 column with the Final column. This single column should hold the final assignment.

This strategy is **cancellation of a possibility by conflict with a given condition.**

The logic table is shown below.

#### Step 7 - Floor assignment of A by exclusion

The job is not over yet, as A is yet to be assigned and also the unassigned floor is conveniently only one, that is, floor 5. So A is assigned floor 5 by exclusion.

The final fully assigned logic table is then,

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

#### Answers

**Question 1.** Who among the following lives on the topmost floor?

Answer 1. Option 3: H.

**Question 2.** Four of the following five are alike in a certain way and hence they form a group. Which one of the following does not belong to that group?

**Analysis:** As among choices G, C, A, D, B, all the four of C, A, D, B live on odd numbered floors they form a group with only G living on an even numbered floor 6. So G does not belong to this group.

Answer 2. Option 1: G.

**Note:** You should be able to identify the key pattern of similar characteristic of the four choice values here.

**Question 3.** Who among the following lives on the fifth numbered floor?

Answer 3. Option 1: A.

**Question 4.** How many persons live between the floors of B and F?

Answer 4. Option 3: 4.

**Question 5.** Who among the following lives exactly between the floors of C and D?

Answer 5. Option 2: F.

**Note:** The detailed explanation seems to be long and consequently the solution time taking. But with clear understanding of the concepts and practised skill in solving this type of problems by applying the collapsed column technique, you should easily be able to solve this problem in well under 5 minutes. In solving the problem in actual test, the table used will only be one. *For explanation we have shown the interim stages as separate tables.*

### Recommendation

The * collapsed column logic analysis technique* is a structured, systematic, clear, and

*for analyzing logic puzzles, family relation problems, floor stay problems and other types of logic analysis problems of any complexity with ease, speed and confidence without creating confusion. But one must be thoroughly conversant with variations of this class of problems by solving the puzzles, family relation or other types of problems using this efficient method. 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.*

**efficient framework****Important note:** The floor stay problem we have solved in this session is comparatively a simple problem. In actual SBI PO test, complexity may be increased by introducing at least one additional characteristic of the persons. But the same process with suitable adaptation can easily deal with such complexities. We will see in a later session how such a problem can be systematically dealt with.

### Tip

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 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**

#### Solved reasoning puzzles

**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 **

**Bank PO type two row hybrid reasoning puzzle solved in confident steps 1**