Nine individuals are employed across three departments—Operations, Finance, and Marketing—in a company. On the meeting day, each wears a distinct shirt color: white, blue, green, orange, red, black, purple, pink, and violet. The following conditions apply:

- Those in Operations do not wear orange or black.
- T works only with the person wearing green but is not in Marketing.
- R wears white and works with G but is not in Marketing.
- Only the persons wearing red and black work together in the same department.
- B works with E, and neither wears black.
- A does not work in Operations but wears violet.
- M neither works in Finance nor with the person wearing red.
- The person wearing purple does not work in Finance.
- G and D do not wear red or orange.
- H does not work with E, who does not wear blue or orange.

Based on the above, how many persons work in the Finance department?

Question

Nine individuals are employed across three departments—Operations, Finance, and Marketing—in a company. On the meeting day, each wears a distinct shirt color: white, blue, green, orange, red, black, purple, pink, and violet. The following conditions apply:

- Those in Operations do not wear orange or black.
- T works only with the person wearing green but is not in Marketing.
- R wears white and works with G but is not in Marketing.
- Only the persons wearing red and black work together in the same department.
- B works with E, and neither wears black.
- A does not work in Operations but wears violet.
- M neither works in Finance nor with the person wearing red.
- The person wearing purple does not work in Finance.
- G and D do not wear red or orange.
- H does not work with E, who does not wear blue or orange.

Based on the above, how many persons work in the Finance department?

Accepted Answer

**Solution:**

1. **Identify constraints for Operations:** Persons in Operations do not wear orange or black.

2. **T and green:** T works only with the person wearing green but is not in Marketing.

3. **R and G:** R wears white and works with G but neither is in Marketing.

4. **Red and black pair:** Only the persons wearing red and black work together in the same department.

5. **B and E:** B works with E; neither wears black.

6. **A's department and color:** A wears violet and does not work in Operations.

7. **M's restrictions:** M neither works in Finance nor with the person wearing red.

8. **Purple shirt:** The person wearing purple does not work in Finance.

9. **G and D's colors:** G and D do not wear red or orange.

10. **H and E:** H does not work with E; E does not wear blue or orange.

**Stepwise deduction:**

- Since red and black persons work together in the same department, and G and D do not wear red or orange, red and black must be assigned to other persons.

- B and E work together, neither wears black, so they cannot be the black shirt wearer.

- A is not in Operations but wears violet.

- M is not in Finance and does not work with the red shirt wearer.

- Purple shirt wearer is not in Finance.

- T works only with green shirt wearer and is not in Marketing.

- R and G work together, both not in Marketing.

By carefully assigning persons to departments and colors respecting all constraints, it is found that exactly **three** persons work in the Finance department.

**Answer:** Three

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