## Analyze the large number of conditions and adopt the right strategies for condition statement execution

In this 11th session on solving reasoning puzzles for SBI PO exams, the puzzle chosen is a floor stay high level reasoning puzzle. To solve this relatively hard puzzle, analysis of the problem, precise selection of the right conditional statement sequence to execute and involved multi-variable elementary logic analysis are required.

Before going ahead, you may refer to our **earlier tutorial sessions and reasonig puzzle solving sessions** from the **linked list provided at the end.**

### High level floor stay Reasoning Puzzle of SBI PO type

#### Problem description

Eight people, A, B, C, D, E, F, G and H live in eight different floors of a building. The lowermost floor is numbered 1, the one above that 2 and so on till the topmost floor is numbered 8. Each one of the persons also owns a different brand of mobile among, Nokia, Pixel, Samsung, Blackberry, Micromax, Lenovo, HTC and Oppo, but not necessarily in the same order. Each person has different birth-months from 1 to 9.

#### Conditional statements

- Birth-month of the person who owns HTC is same as the floor number of the person who owns Lenovo, while the birth-month of the person who owns Lenovo is the same as the floor number of the person who owns HTC.
- Only one person lives between B and and the one who owns Micromax.
- The person who lives in the topmost floor has the highest birth-month.
- The one who owns HTC lives immediately above G.
- G owns neither Lenovo nor Nokia.
- E does not own HTC.
- Only three people live between G and A.
- The one who owns Oppo lives immediately above the one who owns Pixel, but not on the topmost floor.
- The floor number and birth-month are same for the persons who own Micromax and Oppo.
- Only one person lives between F and the one who owns Samsung.
- The number of persons living above F is the same as the number of persons living between F and D.
- Only one person lives between the one who owns Oppo and H.
- Birth-month of the person who owns Samsung is less than three.
- Only two people live between C and the one who owns Nokia.
- Birth-months of the persons who live in the topmost floor and ground floor are square numbers.
- F lives in an odd-numbered floor above the floor numbered four.
- Only three people live between D and the one who owns Lenovo.
- C lives in one of the odd-numbered floors above the one who owns Lenovo.
- The persons who live in floors numbered 4, 6 and 8 have birth-months in multiples of 3.

#### Questions

**Question 1.** Which is the BM value of the person living above H?

- 7
- 8
- 2
- 6
- None of these

**Question 2.** Who lives exactly between E and D?

- B
- C
- F
- G
- A

**Question 3.** Which is the mobile of the person living two floors below C?

- Lenovo
- Oppo
- Nokia
- Blackberry
- None of these

**Question 4.** Who are the owners of Pixel and HTC?

- A and F respectively
- D and C respecively
- G and B respectively
- H and C respectively
- None of these

**Question 5.** What is the mobile of the owner living three floors below the owner of Micromax?

- Blackberry
- Oppo
- Samsung
- Nokia
- None of these

### Solution to the high level floor stay Reasoning Puzzle of SBI PO type

#### Logic table representation

Following is the logic table that we will use for solving the problem.

First column of the above logic table as usual represents floor numbers 1 at the bottom ground floor to top floor number 8. These eight rows formed by the floor numbers will have unique and distinct assignments of three other variables, eight persons, eight mobile types and eight birth-month numbers.

Here floor number is the primary variable against which we place values of other three variables under suitable column only when we are certain that the value belongs to the particular cell.

This is a **compact column logic representation** table in which no cell will remain empty in the final solution.

You may skip the following details of strategy, structures and analysis—useful concepts and methods formed from experience on reasoning puzzle solving.

#### Two degree uncertainties in two cells under same column variable

Though our main aim is to place a value in a cell of the main logic table only when we are certain of it, as a strategy we also place *two degree uncertainties* in * two cells under one column*. For example, if it is certain that either of person A or B lives in floors 2 or 5, we write this two degree uncertainty in both cells as "A/B" and "B/A". This has the advantage of blocking the two cells by the two persons. Cross-column two-degree uncertainties cannot be recorded in the main logic table.

If two-degree uncertainties appear spread over three cells under same column, we won't record it in main logic table but if promising, we will create temporary bonded member structures and record those on the side of the main logic table in the temporary work area. An example is, A lives in floor 7 and B in floor 3 or, A lives in floor 6 and B in floor 2. This is a two degree uncertainty, but spread over four cells. We record it as two Possibilities or Configurations between A and B in the temporary work area.

#### Temporary bonded member structures and Possibilities or Configurations

Forming, recording and enlarging bonded member structures in the temporary work area in solving a reasoning puzzle is generally an essential feature.

For example, when C lives **exactly** between F and A, we get two possibilities, F-C-A and A-C-F. If we know in which floor one of them lives, say C lives in floor 4, we create two promising possibilities, F at 5, C at 4, A at 3 and A at 5, C at 4 and F at 3. In each of the possibilities the positions of the three are certain.

We record these two formations in **two compact columns** on the right side of the main logic table, and continue to search for statements that enlarge these bonded structures with certain assignment of more variable values. This is done by looking for references to A, C or F first using * link search technique, *and continuing the linking through other new variable values. We call these bonded formations each having certain floor placements as

**Possibilities or Configurations**.

By **strategic decision, we don't create more than two possibilities**. This strategy is similar to recording two-degree uncertainty. *Dealing with 3 or more degree uncertainty creates unmanageable confusion in the process of solving such logic puzzles.*

Occasionally *floor separated two possible bonded structures of same variable values* we record below the main table when we don't know floor placement of any of them. These are temporary bonded structures.

**Possibilities are created in the early part of the puzzle solving process and all other temporary structure formation we use later in the puzzle solving process.**

**Reason** is: Possibilities are more promising as these are more certain (we know floor placements within each, even though one of the two will turn out to be invalid later). On the other hand other temporary bonded structures inherently are more uncertain and are used during the later part of the solving process for resolving conflicts.

#### General strategic methods

*When we start solving*, our aim always is to place as many variable values with certainty on the main logic table as possible.

This approach is reasonable. But how do we do it?

We search for statements that provide the first certain placements of **highest amount**. This is **Direct assignment first strategy.**

After getting our first certain placements we search for statements that refer to the already placed values and result in further certain assignments. This technique is common. We call it * Link search technique*.

When no more certain placements are possible * we start creating Possibilities and other temporary bonded structures*. We go on trying to enlarge such structures till we find a statement condition that invalidates one of the structures by conflicting values leaving one combination of values as certain. At this point we

*this certain possibility with the main logic table. This is breakthrough point, and usually after a*

**merge***is achieved, rest becomes easy. There can be more than one breakthrough needed in more complex problems.*

**breakthrough**#### Elementary logic analysis

To decide why between two or three or more possibilities (not Possibility structure with capital P) one is the only true possibility (regarding placement of a value in a cell or invalidating a Possibility, just two scenarios), we need to resort to what is known as elementary logic analysis. In fact this is the foundation of solving reasoning puzzles.

Occasionally chains of elementary logic elements are to be dealt with making things complex.

#### Initial problem analysis

This is a critical part of reasoning puzzle solving. We just don't go into the process of solving a reasoning puzzle starting from the first logic condition. With random approach no self-respecting reasoning puzzle can be solved.

Invariably we have to go through all the given logic conditions to,

- Assess the overall difficulty of the problem.
- Assess which variable values hold more promise for quick resolution.
- Mark the potential worth of the important statements regarding information content or promise of creating certainty.
- Mark which statements need to be executed early and which ones late.
- Identify the primary barrier to overcome.

A sizable reasoning puzzle can be solved with confidence only with careful initial problem analysis followed by strategic and tactical selection of logic analysis sequence.

Let us get down to the main task of processing the conditional statements with the **sole aim of filling up the empty cells as quickly as possible without any confusion and with complete certainty.**

#### Solution Stage 1: Strategy 1: Direct and certain assignment first

In any assignment puzzle, **Direct certain assignments in the beginning is a "highly preferred" priority**. Without such a direct certain assignment of a secondary member to a position, we won't be able to place any member onto the logic table in the beginning, and further steps will be difficult to carry out.

We qualify this strategy with the additional property of a statement first to be executed as one with **direct and certain assignments of maximum amount or maximum number of cells filled up with certainty.**

We select such a statement and process it first to fill up maximum number of empty cells at one go. The advantage is, the more we fill up the empty cells easier does it become to fill up the rest, as uncertainty reduces.

Following this strategy, we process Statement 3 first as it is the only statement that assigns birth-month value of 9 with certainty to the person who lives on 8th floor.

Subsequently we proceed on to execute four more statements consecutively at this stage to create a two degree uncertainty Possibility or Configuration structure and stop. We will show first the result of processing these five statements and then explain why we had chosen the statements and how they affected the logic table status.

The following is the logic table after execution of these five statements in Stage 1.

At the time of initial going through the conditions we noticed the **lightly mathematical statements on birth-month** and decided at that time itself, we would explore these early to see if we can get any certain assignments. Fulfilling the promise, Statement 15 added BM value 4 to floor 1.

In case of Statement 19 though **we achieved a two degree uncertainty** of BM value 3 and 6 over floors 4 and 6. This is an example where we recorded the two degree uncertainties as 3/6 and 6/3 against floor 4 and floor 6. These two degree uncertainties are valuable, as not only these two cells are blocked by these two values, we are also certain that these two values cannot appear against any other floor.

This two degree uncertainty is nearly as good as two clear certainties.

Then Statement 16 caught our attention **because of its limitation of F within top 4 floors**. But due to its attached uncertainty we could place F not in a single cell but in two cells 5 or 7. This is two degree uncertainty of a single variable and is of good value.

Following F, we searched for its occurrence in any other promising statement and located Statement 11 in which D lives below F. The logic analysis created two configurations of F and D at floors, 7, 5 and 5, 1 respectively. Verify whether this is true.

This is an example of two **Possibilities that we recorded as two Configurations** on the right of the main logic table (aligning with proper floor number). While recording we decided to use a single column compact form for recording each configuration.

#### Solution** Stage 2: Strategy of extending the Possibility configurations**

In the absence of any more promising statement, we resorted to search for statements that refer to the configuration values. First Statement 17 referred to D and achieved certain placement of Lenovo at floor 1 in config 1 and along with F at floor 5 in config 2.

Carrying on * link search*, we found in Statement 18 next, C living in one of the odd-numbered floors above the person owning Lenovo. It resulted in certain assignments in both configurations. In config 1 and 2, C got floor 3 and 7 respectively.

Link search next on C located Statement 14 by which we could place Nokia at floor 6 in config 1 and in floor 4 in config 2.

Mark that we have not noted any value in the main logic table. Instead, we have extended the two possible configurations quite a bit with certainty. The placement of the values within each possible configuration is certain. Only problem is, we don't know which possible configuration will become finally valid and which one invalid.

We know this much that one of the two possible configurations must be valid. In future if any condition violates any single value position of a possible configuration, the whole configuration will turn out to be the invalid one, and the second configuration, the valid one.

*Because of the ease of achieving a good amount of certainty at one stroke in future, we create two degree uncertainties in the main logic table or two possible Configurations outside logic table.*

Let us show the status of the resulting logic table after this Stage 2 processing.

#### Solution Stage 3: Certain placement by conflict, elementary logic analysis

Progress till this point has been rather automatic. But now in absence of any further scope of extending the possible configurations, two avenues are open,

- To create more temporary bonded member structures without any floor assigned. These will be floating configurations and will be recorded below the logic table, or,
- To search for a statement that invalidates one of the possible configurations.

Being proactive problem solvers, we chose the second path and decided to explore the effect of **Statement 1.** This is a statement involving **mobiles** of two persons and **inverse relationship between their floor numbers and birth-months**. As it carries a lot of information, we classified it as the most promising statement out of all, at the time of initial analysis itself.

As the two possible configurations are well-populated with values, as well as the main logic table holds some values, we felt this is the right time to give it a try. This is the most promising statement as well as it is the right time to use the statement. The decision follows from **principle of maximum value option.**

After all if a quick trial produces nothing tangible we would be taking the first path, and in any case reach the solution. Otherwise, we would get to the solution faster with invalidation of one possible configuration at this stage itself.

**An example of meaning of Statement 1:** If HTC has floor number and birth month as 3 and 7, Lenovo will have floor number 7 and birth month 3. This is a binding relationship between two pairs of floor number and birth-months.

**Elementary logic analysis,**

Out of HTC and Lenovo, Lenovo has its floor assigned in both the possible configurations, but its floor number 1 and BM value 4 combination is invalid for configuration 1, as floor number 4 is locked in the two degree uncertainty of 3/6 of BM value, and can't have BM 1. While analyzing possible configurations we have to read the corresponding certain values from the main logic table. Possible configuration 2 doesn't have such conflict and must be the

valid combination to be mergedwith the main logic table.

This is the **first major breakthrough.**

In the figure below, we still keep configuration 2 for ease of verifying the merging.

The logic table after Stage 3 is shown below.

#### Solution Stage 4: Placing a two-degree bonded member structure on the logic table

At this stage after the first breakthrough, we took up the next promising **Statement 7**. "Only three people live between G and A". It would have created a floating two member bonded structure with too many possible placements **earlier in an empty table**. But now after resolving the possible configurations, the **Person column of logic table** is fairly filled up. We felt it the right time to take up this promising statement to achieve certain placement of A and G in some way in this constrained situation of less number of available positions.

Any statement that creates a bonded member structure is promising, but when it is to be executed depends on the uncertainties associated with the statement as well as the filled-up state of the logic table.

At this Stage 4, just after Stage 3 execution, Statement 7 that directly relates **two persons separated by a three floors is the most promising statement.**

**As a rule,** after a cursory analysis of the statement selected, we look for **further linked statements** referring to a member of the current statement. Here also after a cursory analysis we located such a Statement 4. "The one who owns HTC lives immediately above G" in which G is referred to in a short bond that extended the A-G bonded member structure.

Let us show first the result of execution of Statement 7 and 4 at this stage and will then provide the details of elementary logic analysis involved.

We could successfully place A and G as a two degree uncertainty (that we also call a Cycle) in floor 2 and 6 as G/A and A/G. Following is the **elementary logic analysis.**

**Conclusion:** In the Person column, with present vacancy position, G/A can take "floor 2 and floor 6" or "Floor 4 and floor 8". *With HTC immediately above G we had useful conflicts now.*

Reasoning,

Because of conflict at Lenovo with HTC, G can't be in 4. Also it can’t take floor 8 as HTC above it will be out of the table. So the only feasible option is, G/A in 2 and A/G in 6. We are not yet in a position to fix exact floors of G and A.

#### Solution Stage 5: Elementary logic for certain placement of A and G

In reality we could, but to show the logic analysis in more detail a new Stage 5 is created and explanation follows it.

We have achieved as much as we can with the last pair of statements by placing the two degree uncertainty couple of A/G in floor 2 and 6. Now we remember that we **haven't really processed the rich promising Statement 1 fully.**

After Stage 4, to fulfill the **inverse relation** between floor number and BM of HTC and Lenovo, we take stock of available options and carry out the complete logic analysis:

Among available BM and floor values, only 2 and 7 are available for this relationship to be true. 1-4 invalid, 3-6 invalid, 8-9 invalid. Out of 2,5,7, Lenovo has taken 5. So 2, 7 BM and floor are available for HTC. By statement 4, HTC lives immediately above G. So it cannot take floor 2 (as G would have to be in floor 1 then); and so HTC must take floor 7 with BM 5, and Lenovo at floor 5 assigned BM 7. Position of G is also ascertained indirectly now to be at floor 6 and so A at floor 2. Two-degree uncertainty or cycle of A/G is thus finally resolved.

A lot has been achieved at this** second breakthrough.**

This stage being over we will proceed to the next stage with the goal of specifying mobile column more. It is the comparatively empty column.

#### Solution Stage 6: Placing mobiles with certainty using promising position and BM linked statement and link search

During initial problem analysis we marked two floor position and BM linked statements, Statement 1 and Statement 9. The first has been fully exploited. It is time now to use **Statement 9.** "The floor number and birth-months are same for the persons who own Micromax and Oppo".

It limits Micromax and Oppo to floors 2 and 6, but by linked **Statement 8.** "The one who owns Oppo lives immediately above the one who owns Pixel, but not on the topmost floor." Oppo cannot be placed at 6 as Pixel below it will have conflict with Lenovo at 5. So Oppo must be at floor 2, Pixel at floor 1 and Micromax at floor 6.

This is another piece of **elementary logic analysis.**

Status after this stage is shown below.

#### Solution Stage 7: Routine assignments of the rest of values

With most of the cells filled up, task at this stage is routine. We will execute four statements 10, 13, 12 and 2 in sequence.

By Statement 10, having floor 7 position blocked by HTC, Samsung can take only floor 3, and by statement 13 it gets only possible BM value of 1.

Remaining mobile out of 8 is Blackberry. It goes to only vacant position at floor 8.

By Statement 12 H gets only possible floor 4.

By Statement 2, B gets floor 8 and remaining person E in remaining floor 3 by Principle of exclusion.

Solved.

**Note:** BM value 8 remained unused.

#### Answers to the questions

**Question 1.** Which is the BM value of the person living above H?

Answer 1. Option 1: 7.

**Question 2.** Who lives exactly between E and D?

Answer 2. Option 5: A.

**Question 3.** Which is the mobile of the person living two floors below C?

Answer 3. Option 1: Lenovo.

**Question 4.** Who are the owners of Pixel and HTC?

Answer 4. Option 2: D and C respectively.

**Question 5.** What is the mobile of the owner living three floors below the owner of Micromax?

Answer 5. Option 3: Samsung.

### Comment

This is a relatively hard puzzle because of fairly large number of object sets 4 (floor, person, mobile and birth-month), fairly large number of objects in each set 8, and quite large number of conditional statements 19. It might seem at first glance unsolvable, but with good initial problem analysis, well-developed strategies and tactics in selecting the right statements at the right stage, and good skill in elementary logic analysis, one should not find it very difficult.

Two statements "5. G owns neither Lenovo nor Nokia." and "6. E does not own HTC." turned out to be superfluous and indirectly verified the solution by not producing any contradiction. These were not taken up earlier because of their high uncertainty and resulting weak value. The superfluity indirectly showed the efficiency of the solution path.

Overall, this is a good puzzle to solve as it has considerable amount learning promise.

### 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 reasoning puzzles for SBI PO quickly 8**

**How to solve high level box positioning reasoning puzzle for SBI PO quickly 9**

#### Solved reasoning puzzles SBI PO type

**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**

**SBI PO type high level floor stay reasoning puzzle solved in confident steps 11**

#### Solved reasoning puzzles Bank PO type

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

**Bank PO type four variable basic assignment reasoning puzzle solved in a few steps 2 **

**Bank PO type basic floor based reasoning puzzle solved in a few steps 3**

**Bank PO type high level floor stay reasoning puzzle solved in quick steps 4**