Introduction Generic Puzzles - Logical Reasoning (LR) & Data Interpretation (DI)

Introduction

• Generic puzzles refer to a broad category of logical‑reasoning problems that do not fall neatly into fixed templates such as seating arrangements or games & tournaments.
• They typically involve one or more of the following types of tasks:
  • Scheduling: Assigning tasks, events, or people to specific time slots or roles based on constraints.
  • Grouping & Selection: Forming teams or selecting individuals/items while adhering to rules (for example, mutual exclusions or dependencies).
  • Sequencing: Determining the correct order of events or items using given conditions.
  • Conditional Logic: Applying if–then, either–or, or neither–nor statements to deduce outcomes.
  • Constraint‑Based Problems: Solving scenarios where certain conditions must be satisfied (for example, “A cannot be with B” or “C must be selected if D is selected”).

Common Characteristics of Generic Puzzle Questions

• Multiple constraints: Typically 5–8 conditions that must be applied simultaneously.
• No fixed template: Unlike certain standard puzzle types there is no one‑size‑fits‑all approach; each puzzle needs fresh analysis.
• Option‑based elimination: Many puzzles are multiple‑choice, enabling elimination of impossible options quickly.
• Variable complexity: Problems range from straightforward logical deductions to deep case‑based analysis requiring careful tracking of possibilities.

Step‑by‑Step Approach

To solve generic puzzles efficiently, follow a structured sequence combining careful reading, organised representation, and systematic elimination.

• Read the Entire Question Carefully: Identify the problem type, scope, and key constraints to train pattern recognition.
• List All Conditions: Write each rule separately using logical deduction, noting dependencies like “If A then B” or “A ≠ B.”
• Start with the Most Restrictive Clue: Begin with the clue that eliminates the most possibilities, applying an elimination strategy.
• Visualise the Setup: Use grids, timelines, or placeholders to clearly represent relationships, enhancing visualisation skills.
• Build Scenarios: Use case-based reasoning when conditional statements create multiple possibilities; keep each case organised and consistent.
• Apply Elimination: Reject answer choices that violate any rules to quickly narrow down valid solutions.
• Re-evaluate After Each Step: Check consistency at every stage and manage time by deciding when to move on if progress stalls.

Solved Examples

The following illustrations provide worked solutions to typical puzzle questions. Attempt each question yourself before reading the solution.

Illustration 1

Direction: At a fancy dress party, Mr. Abhimanyu, Mrs. Bablu, Mrs. Chanchal, Mr. Dyan, and Mr. Elite attended. They dressed as specific objects representing their professions: a leaf, a pen, a fork, a camera reel, and a stethoscope. The corresponding professions were photographer, gardener, compounder, teacher, and cook.
Given clues:
(i) Mr. Abhimanyu is a teacher.
(ii) Neither Mrs. Bablu nor Mrs. Chanchal was dressed as a fork.
(iii) None of the men is a compounder.
(iv) Mr. Dyan is dressed as a camera reel.
(v) Mrs. Chanchal is a gardener.
(vi) Each person wore a costume relevant to his profession only. For example, the pen was worn by the teacher, the camera reel by the photographer, etc.
Q1: Which person is dressed as a stethoscope?
(a) Mr. Abhimanyu
(b) Mrs. Bablu
(c) Mrs. Chanchal
(d) Mr. Dyan
Q2: What is Mr. Elite's profession?
(a) Cook
(b) Gardener
(c) Compounder
(d) Teacher

Sol: 

Step 1: Record the direct clues.

Step 2: Assign remaining costumes and professions.

• 

The solutions are:

Sol 1:  Option (b) is correct. 
Mrs. Bablu.

Sol 2:  Option (a) is correct. 
Elite is the cook.

Illustration 2

Directions: Read the information and answer the question.
Four engineers, designated as CE, SE, EE and AE, read a certain number of newspapers early in the morning.
One of them reads four newspapers, another reads three newspapers, the third reads two newspapers while the fourth one reads one newspaper. Below are some additional facts regarding the names of these officers:
(i) Naina is not the EE.
(ii) Hamleys is the AE.
(iii) Naina is not the CE and he reads more number of newspapers than Lalu.
(iv) The one who is the CE, reads more number of newspapers than Lalu .
(v) The person, who is the SE reads the maximum number of newspapers.
(vi) Bryan does not read two newspapers.

Q: Which of the following statements is necessarily true?
(a) Hamleys is the AE and reads two newspapers.
(b) Lalu is the EE and reads one newspaper.
(c) Bryan is the CE and reads three newspapers.
(d) Naina is the EE and reads four newspapers.

Sol: Hence, option (c) is the correct answer.

Explanation:

1. From (ii): Hamleys = AE.
2. From (v): SE reads the maximum (4) newspapers.
3. From (i) and (iii): Naina is not EE or CE, and Naina reads more newspapers than Lalu. Therefore Naina must be the SE and so reads 4 newspapers.
4. From (iv): The CE reads more newspapers than Lalu, so CE cannot be Lalu. Since Naina is SE and Hamleys is AE, remaining names for CE and EE are Bryan and Lalu. Thus Lalu must be EE and Bryan must be CE.
5. From (vi) Bryan does not read 2 newspapers. Available counts left are 3 and 1. CE must read more newspapers than Lalu (EE). Hence Bryan (CE) reads 3 and Lalu (EE) reads 1. Hamleys (AE) must then read the remaining number (2).

Final distribution:

Engineer	Name	No. of Newspapers
AE	Hamleys	2
CE	Bryan	3
SE	Naina	4
EE	Lalu	1

Solved Examples 

Instructions for Questions 1-4

Four institutes, A, B, C, and D had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts.
I. Vendor Z had at least one contract in every year.
II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.
III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.
IV. There were ve contracts in 2012.
V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4-year contract, and A and C had one 3-year contract each. The other four contracts were single-year contracts.
VI. Institute C had one or more contracts in 2012 but did not have any contracts in 2011.
VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contracts in 2010. 

Q1: In which of the following years were there two or more contracts?
(a)  2017  
(b) 2016
(c)  2015
(d)  2018  

Sol: Option (c) is correct.

Explanation:

Hence option (c) 2015 is correct.

Que 2: Which institutes and vendors had more than one contracts in any year?
a. B, W, X, and Z
b. A, B, W, and X
c. A, D, W, and Z
d. B, D, W, and X  

Sol: Option (b) is correct.

Explanation:

Based on multi-year and single-year contract distribution as in Q1, institutes A, B and vendors W, X had multiple contracts in the same year.

Que 3: In how many years during this period was there only one contract?
a. 3
b. 2
c. 4  
d. 5  

Sol: Option (a) is correct.

Explanation: Years with single contracts were 2016, 2017, and 2018, totalling 3.

Que 4: Which of the following is true?  
a. B had a contract with Z in 2017
b. B had a contract with Y in 2019
c. D had a contract with X in 2011
d. D had a contract with Y in 2019

Sol: Option (d) is correct.

Explanation: According to the contract schedule, D had a contract with Y in 2019.

Solved Examples — Group Testing (Questions 5–8)

Instructions for Questions 5-8

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed. 

If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease. 

Que 5: Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials. Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?
a.  {5,6,7,8}
b.  {4,5,6,7}
c.  {4,5,6,7,8}
d.  {4,5}   

Sol: Option (c) is correct.

Explanation:

1. If the diseased patient's blood is mixed with another sample that appears in multiple vials, the number of positive vials can vary widely depending on which patient was mixed and the overlap of vials. The maximum is 8 (if the mixture causes all vials that include either patient to be positive).
2. Working through possible mixing patterns yields achievable counts of 4, 5, 6, 7 and 8 positive vials. Thus the full possible set is {4,5,6,7,8}.

Que 6: Which of the following combinations of test results is NOT possible?
a. Vials A and E positive, vials C and D negative
b. Vial B positive, vials C, F and H negative
c.  Vials A and G positive, vials D and E negative
d.  Vials B and D positive, vials F and H negative 

Sol: Option (a) is correct.

Explanation:

Use the vial membership lists (these are the mapped sets):

• Vial A: 9,10,11,12,13,14,15,16
• Vial B: 1,2,3,4,5,6,7,8
• Vial C: 5,6,7,8,13,14,15,16
• Vial D: 1,2,3,4,9,10,11,12
• Vial E: 3,4,7,8,11,12,15,16
• Vial F: 1,2,5,6,9,10,13,14
• Vial G: 2,4,6,8,10,12,14,16
• Vial H: 1,3,5,7,9,11,13,15

If vials C and D are negative, then none of the patients in those vials can be infected. That eliminates every patient present in C or D. But A contains only patients who all appear also in C or D except possibly none—so A cannot be positive if C and D are both negative. Hence the combination A and E positive with C and D negative is impossible.

Que 7: Suppose vial A tests positive and vials D and G test negative. Which of the following vials should we test next to identify the patient with the disease?
a. Vial B
b. Vial E
c. Vial C
d. Vial H  

Sol: Option (b) is correct.

Explanation:

1. If A is positive and D, G are negative, the intersecting membership lists reduce the candidates to {13,15}.
2. Check which vial discriminates between 13 and 15:
   • Vial B does not contain 13 or 15 — so it gives no information.
   • Vial C contains both 13 and 15 — so it cannot distinguish.
   • Vial H contains both 13 and 15 — so it cannot distinguish.
   • Vial E contains only patient 15 (from the two candidates); thus testing E will tell us whether 15 is infected (E positive) or else 13 is infected (E negative).

Therefore test Vial E next.

Que 8: Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
a. Patient 14
b. Patient 8
c. Patient 6
d. Patient 2  

Sol: Option (c) is correct.

Explanation:

1. Vial C contains {5,6,7,8,13,14,15,16} and is positive.
2. Vials A, E and H are negative, which eliminates any patient appearing in A, E or H.
3. Among the members of C, every patient except 6 also appears in at least one of A, E or H. Therefore patient 6 is the only remaining candidate and must be the infected one.

Instruction for Question 9-11:

Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O & Q
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi

Que 9: Which two candidates can belong to the same department?
a. Prof. Pakrasi & Prof. Qureshi 
b. Prof. Pakrasi & Prof. Samuel
c. Prof. Qureshi & Prof. Ramaswamy
d. Prof. Ramaswamy & Prof. Samuel

Sol: Option 'a' is correct

Explanation: 

Given the constraints, Marketing & Strategy (M&S) has 2 candidates, who voted for others outside their department. Pakrasi and Qureshi are inferred to both be from M&S.

They are the only pair that comply with the voting and department rules.

Que 10: Which of the following can be the number of votes that Prof. Qureshi received from a single department?
a. 7
b. 6
c. 8
d. 9

Sol: Option 'd' is the correct answer.

Explanation: The only feasible voting blocks for Qureshi include 9 votes from a single department (M&S), fitting all constraints on candidate distributions and voting patterns.

Que 11:  If Prof. Samuel belongs to B&H, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q
a. Neither statement A nor statement B
b. Only statement B
c. Only statement A
d. Both statements A and B

Sol: Option 'd' is correct

Explanation: 

Given Samuel in B&H and voting pattern, Pakrasi belongs to M&S and Ramaswamy to O&Q. Both statements are true under these assumptions.