## A simple adaptation of the compact logic table deals with the one to many assignments

In this sixth session on solving a SBI PO type high level reasoning puzzle in a few easy and confident steps without confusion, the puzzle chosen does not have all its assignment relations one to one. Among four object sets, two objects sets have same valued members. This creates groups or more formally one to many relationships. A simple adaptation of the minimal logic table deals with this special situation easily.

For detailed concepts on the fundamental techniques and strategies used 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 with one to many relations: Who visits which city, takes which person as wife and has how many children?

#### Problem description

Six husbands M1, M2, M3, M4, M5 and M6 went on trips with their wives F1, F2, F3, F4, F5 and F6 and with their children, but not necessarily in the same order. Four families went to different tourist places, Gangtok, Dalhousie, Jaldapara, Puri and two of the families went to Srinagar. Two of the pairs didn't have any child, two had one child each and the other two pairs had two and three children each in no specific order.

#### Conditional statements

- M1 and M4 visited Srinagar but they did not have either zero or three children.
- M6 did not go with F5 and both of them did not have two children.
- F4 and F3 went to Gangtok and Jaldapara respectively.
- The persons visiting Dalhousie had the same number of children as M2 did.
- M3 went with F6 to Dalhousie but did not have either one or three children.
- M2 went to Gangtok and had no child.
- M5 did not go either with F1 or with F2. He did not go to Jaldapara and he had neither one nor two children.

#### Questions

**Question 1.** Who among the following went to Gangtok?

- F5-M5
- M4-F1
- M3-F6
- M2-F4
- None of the above

**Question 2.** If M1 went with F1 then who among the following went with M4?

- F3
- F4
- F2
- F5
- None of the above

**Question 3.** Who among the following went to Dalhousie?

- F5
- F6
- F3
- F4
- None of the above

**Question 4.** How many children did M3 have?

- one
- three
- zero
- two
- None of the above

**Question 5.** Which of the following combinations is correct?

- M5-Puri-three
- F3-Dalhousie-one
- M6-Gangtok-three
- M3-Srinagar-two
- None of the above

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

### Solution to the SBI PO type high level Reasoning Puzzle with one to many relations: Problem analysis and representation

The number of objects is four (more than four usually is hard) and number of logic conditions is only seven (more the number of logic conditions more is the scope of confusion in general).

The specialty of the problem lies in two families having no child, two families 1 child and two families both going to Srinagar. *This forms three groups which create one to many relations. This new aspect along with small number logic conditions alerts us for careful formation of the strategy of logic condition execution.*

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

Husbands form the column labels while the Wives form the first row members (it can be opposite also). These two sets have each six members with one to one distinct relationships. But distinct cities are 5 in number with two families going to Srinagar. Similarly, in number of children we have two such value repetitions in "zero" and "one".

Cities and Children (number of) form the second and third six cell rows in the logic table with only modification in the list of cities and list of number of children written at the top of the table. In these lists, Srinagar is repeated twice, number of children "zero" and "one" both repeated twice to complete number of members in each to six.

With this change we will be able to carry out the logic analysis and assignment activities following the normal strategic methodology.

#### Solution Stage 1: Strategy 1: Direct assignment first strategy without increasing uncertainty

We always want to make certain assignments without introducing any uncertainty at the very start. By this direct assignment first strategy, the **Statement 6.** "*M2 went to Gangtok and had no child.*" enables us to assign Gangtok to second column of City row with zero as number of children.

#### Solution Stage 1: Strategy 2: Statement group execution with link search technique to achieve assignment with certainty

Next we identify **Statement 5.** "*M3 went with F6 to Dalhousie but did not have either one or three children.*" as a **direct assignment statement** but with fair degree of uncertainty. To reduce the uncertainty we look for any reference to F6 or Dalhousie, the two certain assignments in Statement 5. As a result of link search we get **Statement 4.** *"The persons visiting Dalhousie had the same number of children as M2 did."* which links to Children value of certain assignment for M2 through Dalhousie, a very desirable result.

Together, the two statements enables assignment of F6, Dalhousie and "zero" to the three cells of M3 column.

#### Solution Stage 1: Strategy 3: Direct assignment with uncertainty

Statements making direct assignments are always given priority but we choose such a statement for the current execution step depending on its degree of uncertainty. In the first stage, if possible, we don't accept any uncertainty in direct assignment statement at all. In subsequent steps we relax this restriction as we have already assigned values which might help to transform an uncertainty into a certainty.

Thus, at every step the

, one or more than one.primary objective is to achieve certain assignments

In previous step we have used a direct assignment statement with uncertainty but having found a useful link in a second statement we have decided to execute the two statements together to achieve certainty ultimately.

In this third step, finding no way to achieve fully certain assignments we choose a direct assignment **Statement 1.** *"M1 and M4 visited Srinagar but they did not have either zero or three children."* with uncertainty but with maximum number of direct assignments. It is a compromise, but a fruitful compromise.

Assignment of Srinagar as City value to M1 and M4 is straightforward. But let us carefully evaluate the number of children situation on execution of this statement. As number of children for these two husbands cannot be zero or three, the values left will be "one", "one" and "two" for the two columns. So the possibilities will be three for these two columns, "one-one", "one-two" or "two-one". Check this step carefully.

Notice that we have started to consider a **three degree uncertainty** in the two columns thus* deviating from our two degree uncertainty principle*. The number of statements left being small we expected resolution of this higher degree uncertainty quickly. Furthermore even though number of possible combinations for two columns is three, the values involved are only two in number. That should also aid quick uncertainty resolution.

The logic table after this stage is as below,

**Solution Stage 2: Strategy 4: Assignment by negation on a largely filled up favorable zone**

In Stage 2, we focus our attention on City row which is fairly filled up with four cells assigned out of 6. On quick scan, **Statement 7.** *"M5 did not go either with F1 or with F2. He did not go to Jaldapara and he had neither one nor two children."* could be used for achieving the certain assignment of City Puri to column M5. This happens because we had only two City values left, out of which one is negated resulting in the other to be a certainty. Frequently we use this strategy to achieve a certain assignment on a largely filled up row or column as the case may be.

Here the largely filled up row of City is the * favorable zone* on which we apply the negation of one of the two values. This terminology is borrowed from our Sudoku problem solving experience where this strategy is frequently employed.

Let us fully evaluate the effect of Statement 7. M5 gets city Puri and by * principle of exclusion* M6 gets city Jaldapara, the only value left. That is easy. But we have to deal with two sets of uncertainties now.

The first part says, *"M5 did not go either with F1 or with F2." *which leaves three values F3, F4 and F5 for M5 (as F6 is already assigned). Again we accept a three degree uncertainty. Notice the technique of complementing here. *Instead of recording the negative statement results, we have converted it to a set of positive assignment possibilities* using the **set complementing** operation (not F1 or F2 means other members of Wives set, F3, F4 and F5 with F6 already assigned).

Positive assignments are generally preferable compared to negative assignments. That is why we have resorted to this * negative logic condition transformation*.

Let us now resolve the third part of the compound statement 7.

The third part says, "*he had neither one nor two children."* which immediately fixes "three" as number of children for M5 using negative logic condition transformation and set complementing.

**Check these steps yourself.**

The logic table now looks like,

**Solution Stage 3: Strategy 3: **Direct assignment with uncertainty

Out of two statements left priority is given to the one with direct column assignment, that is, **Statement 2.** "*M6 did not go with F5 and both of them did not have two children."* which has a good amount of uncertainty so much so that we had to record "not F5" in first row for M6 as well as "F5: not two" even outside the logic table. Rarely we have to record such an uncertainty outside the logic table because we are unable to place it against any column.

But the positive certain assignments we get are in the area of number of children. As it cannot be two for M6, it can only be one (negative logic condition transformation coupled with set complementing). As soon as one number of "one" is assigned to M6, *the number of possibilities in M1 and M3 gets reduced to two*, "one-two" and "two-one". This is * uncertainty cancellation*.

Check this step yourself.

The logic table after this stage of execution is as below,

**Solution Stage 4: Strategy 5: **Piggybacking on secondary members

We are now left with a single **Statement 3.** *"F4 and F3 went to Gangtok and Jaldapara respectively.*" which being assignments on Wives, a set of secondary members, we were unable to place the assignments against any column till the City row got fully filled up. Now riding on the assigned secondary values of Gangtok and Jaldapara F4 and F3 can be assigned with certainty to M2 and M6 respectively. This is why we name this strategy as Piggybacking on secondary members.

Again, M6 getting F3, out of three possibilities in M5, namely, F3, F4 and F5, two get cancelled and we get the certain assignment of F5 in M5. This is uncertainty cancellation.

Nothing more can be done on the logic table and its final state is as follows,

This is a special case of a final logic table where uncertainties still exist in columns M1 and M4. Unable to fully assign the logic table by taking further steps, we expect the deficiency to be taken care of in the questions asked.

Let us answer the questions then.

#### Answers to the questions

**Question 1.** Who among the following went to Gangtok?

Answer 1. **Option 4:** M2-F4.

**Question 2.** If M1 went with F1 then who among the following went with M4?

Answer 2. **Option 3:** F2. This is the question where, as expected, the remaining uncertainty has been used intelligently. Answer value by uncertainty cancellation.

**Question 3.** Who among the following went to Dalhousie?

Answer 3. **Option 2:** F6.

**Question 4.** How many children did M3 have?

Answer 4. **Option 3:** zero.

**Question 5.** Which of the following combinations is correct?

Answer 5. **Option 1:** M5-Puri-three.

This deceptively simple looking problem has in it a good amount of new learning.

**Broadly, two points come out,**

- One to many assignments complicate any logic assignment problem.
- If additionally the number of statements is small, one needs to be extra careful.

Overall we call this strategic analytical methodology for reasoning puzzle solving systematically as the **Collapsed column logic analysis technique.**

### 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.*

### 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**