The 8 Employees in 3 Departments Reasoning Puzzle from SBI PO exams has nine Cues to answer 5 questions. To solve easily, identify suitable primary object.
8 Employees in 3 Departments Reasoning Puzzle
Description
A, B, C, D, E, F, G and H are employees in an organization belonging to three departments, namely Administration, Finance and Marketing such that not more than three employees work in the same department. Each of them has a different choice of sports namely, Badminton, Cricket, Football, Basketball, Hockey, Volleyball, Lawn tennis and Table tennis but not necessarily in the same order.
Clues:
- D works in Administration and does not like either football or cricket.
- F works in Finance with only A who likes table tennis
- E and H do not work in the same department as D.
- C likes hockey and does not work in Marketing.
- G does not work in Administration and does not like either cricket or badminton.
- One of those who work in Administration likes football.
- The one who likes volleyball works in Finance.
- None of those who work in Administration likes either badminton or lawn tennis.
- H does not like cricket.
Questions
Question 1. Which of the following groups of employees work in Administration?
- EGH
- AF
- BCD
- BGD
- Data insufficient
Question 2. Which of the following combinations of employee-department-favorite sport is correct?
- E-Administration-cricket
- F-Finance-lawn tennis
- H-Marketing-lawn tennis
- B-Administration-table tennis
- None of the above
Question 3. In which department does E work?
- Finance
- Marketing
- Administration
- Data insufficient
- None of the above
Question 4. What is E's favorite sport?
- Cricket
- Badminton
- Basketball
- Lawn tennis
- None of the above
Question 5. What is G's favorite sport?
- Cricket
- Badminton
- Basketball
- Lawn tennis
- None of the above
Hints:
- Employees each like a different sport: One-to-one relationship.
- But, the eight employees belong to 3 departments.
- The Department-to-Employee relationship is One-to-many.
- This one-to-many relationship makes the design of the simple and most convenient assignment table a critical element to the optimal and efficient solution.
- Think of how to convert the one-to-many relationship into a simple structure for representing the assignments.
Solution to 8 Employees in 3 Departments Reasoning Puzzle: Preparation
Understanding the problem: Objects, Relationships and Showing Assignments
- Employee (8 values), Department (3 values) and Sport (8 values) are the three objects.
- An Employee works in a department and likes a Sport. This forms a unique Employee-Department-Sports relationship.
- Ultimate objective: Discover and show the 8 such unique three-valued relationships in a table.
- The simplest way to do this is to use a virtual Position number from 1 to 8 as the column header and place all new relationships between two or three objects under any unoccupied position.
- Relative position having no importance here, freedom of noting and analyzing the newly discovered relationships will be maximum in this form of the assignment table.
Accordingly, the most convenient assignment table at the start is:
Solution to 8 Employees in 3 Departments Reasoning Puzzle: Clue Analysis and Assignments
Stage 1: Direct Assignments first and Elementary logic analysis
Clue 1. "D works in Administration and does not like either football or cricket."
- Result: D in Admin and D "not football or cricket". It is important to record the negative assignments. D and Admin placed in position 1 with "not football or cricket" in Sports row.
Clue 2. "F works in Finance with only A who likes table tennis."
- Result: Only F and A are in Finance department and A likes table tennis. F and Finance placed in position 2 and A, table tennis and Finance in position 3.
Clue 4. "C likes hockey and does not work in Marketing."
- Result: C likes hockey. With Finance filled up, C must be in Admin. C, hockey and Admin placed in position 4.
Clue 6. "One of those who work in Administration likes football."
- Result: One unknown employee in Admin likes football. Admin and football placed in column 5 with Employee still unknown This shows the advantage of position as header.
Clue 7. "The one who likes volleyball works in Finance."
- Result: With F and A only in Finance and A liking table tennis, F must be liking volleyball in position 2.
Stage 1 assignment table:
Stage 2: Assignments by Conflicts, Elimination and Defaults
Clue 8. "None of those who work in Administration likes either badminton or lawn tennis."
- Result: D likes basketball.
- Reason: D, C and an unknown employee work in Admin. With C and the unassigned employee already liking a sport not badminton or lawn tennis, D must be the one with dislike of the two. D dislikes badminton, lawn tennis, football and cricket. The only sport left for D among badminton, lawn tennis, cricket and basketball not liked yet is basketball.
Clue 3. "E and H do not work in the same department as D."
- Result: E and H are in Marketing. Placed in positions 6 and 7.
- Reason: D is in Admin and Finance is filled up leaving only Marketing for the E and H.
Clue 5. "G does not work in Administration and does not like either cricket or badminton."
- Result: G in Marketing and likes lawn tennis. G, lawn tennis and Marketing placed in position 8.
- Reason: Finance is full and G does not work in Admin. Marketing is left for G. Out of the three Sports not yet liked: cricket, badminton and lawn tennis, G dislikes cricket and badminton leaving lawn tennis for him.
- Additional deduction: The only left out Employee B must be in the only unoccupied position 5. Position 5 employee already work in Admin and likes football. This is an assignment by default.
Clue 9. "H does not like cricket."
- Result: With cricket and badminton not yet liked, cricket is eliminated for H by the clue, leaving badminton for him. The only sport left cricket must be for E—cricket for E and badminton for H.
Completed assignment table:
Answers to the questions
Refer to the completed assignment table shown above for answers.
Question 1. Which of the following groups of employees work in Administration?
- Options: 1:EGH, 2:AF, 3:BCD, 4:BGD, 5:Data insufficient
Answer 1. Option 3: BCD.
Question 2. Which of the following combinations of employee-department-favorite sport is correct?
- Options: 1:E-Administration-cricket, 2:F-Finance-lawn tennis, 3:H-Marketing-lawn tennis, 4:B-Administration-table tennis, 5:None of the above
Answer 2. Option 5: None of the above. E is in Marketing, not Administration; F likes volleyball, not lawn tennis; H likes badminton, not lawn tennis; B likes football, not table tennis leaving only the Option 5: None of the above.
Question 3. In which department does E work?
- Options: 1:Finance, 2:Marketing, 3:Administration, 4:Data insufficient, 5:None of the above
Answer 3. Option 2: Marketing.
Question 4. What is E's favorite sport?
- Options: 1:Cricket, 2:Badminton, 3:Basketball, 4:Lawn tennis, 5:None of the above
Answer 4. Option 1: Cricket.
Question 5. What is G's favorite sport?
- Options: 1:Cricket, 2:Badminton, 3:Basketball, 4:Lawn tennis, 5:None of the above
Answer 5. Option 4: Lawn tennis.
Comments
This tricky reasoning puzzle is from a Bank Probationary Officers' (Bank PO) recruitment exam and should be enjoyable to puzzle enthusiasts and puzzle lovers as well.
Design of the simple assignment table not only enabled quick and painless solution, answering the three-valued question like question 2 was also dead easy.
The key lies in showing each of the 8 sets of the unique three related values (the triplets) separately and distinctly.
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