Nine persons work in three departments i.e., operations, finance and marketing of a company. On their meeting day, they wear different color shirts i.e., white, blue, green, orange, red, black, purple, pink and violet. All the information is not necessary in the same order as given.

The persons work in operations do not wear orange and black. T works only with the one wearing green but not in marketing. R wears white and work with G but not in marketing. Only the persons wearing red and black work together in same department. B works with E and none of them wear black. A does not work in operations but wears violet. M neither works in finance nor with the one wearing red. The one wearing purple does not work in finance. G and D do not wear red and orange.

H does not work with E who does not wear blue and orange.

If M and the one wearing purple interchange their departments with E and G, then name the persons (with their shirt color) who will work in operations department?

Correct Answer: G-blue, E-pink

Let's deduce the department and shirt color for each of the nine persons step-by-step based on the given clues.

Step 1: Identify the basic constraints on departments.
There are three departments: Operations, Finance, and Marketing.
There are 9 persons in total.

Step 2: Analyze T's department and team.
Clue: "T works only with the one wearing green but not in marketing."
- Since T does not work in Marketing, T must work in either Operations or Finance.
- "T works ONLY with..." means T's department has exactly 2 persons in total: T and the person wearing Green.
- Thus, T and Green form a two-person department.

Step 3: Analyze the "Red and Black" clue.
Clue: "Only the persons wearing red and black work together in same department."
- This means the persons wearing Red and Black form another department consisting of ONLY those 2 people.
- Therefore, we have two departments with exactly 2 persons each, and the third department must have the remaining 5 persons (since 2 + 2 + 5 = 9).

Step 4: Analyze R and G's department.
Clue: "R wears white and work with G but not in marketing."
Clue: "G and D do not wear red and orange."
- R wears White. Since R works with G, R's department contains at least R and G. Neither R nor G wears Red or Black.
- Since R does not work in Marketing, R must work in Operations or Finance.
- R and G cannot be in the 2-person Red/Black department (R wears White).
- R and G cannot be in T's 2-person department because T works ONLY with the person wearing Green (and R wears White, not Green).
- Therefore, R and G must be in the large department of 5 persons!
- Since R does not work in Marketing, the 5-person department must be either Operations or Finance.

Step 5: Determine which department has how many persons and who is where.
- The 5-person department is NOT Marketing (since R is in it and R is not in Marketing). So Marketing must be one of the two-person departments.
- Let's check T's department: T works in Operations or Finance. T's department has 2 persons (T + Green).
- Red & Black department has 2 persons.
- So the department sizes are: 5, 2, 2.
- Let's place the departments:
- R and G (and others) are in the 5-person department.
- Clue: "A does not work in operations but wears violet."
- Clue: "M neither works in finance nor with the one wearing red."
- Clue: "The persons work in operations do not wear orange and black."

Let's map out the 5-person department:
- B works with E and none of them wear black.
- So B and E are together.
- Since B, E, R, G must be together in the 5-person department (as 2-person departments can only hold {T, Green} and {Red, Black}):
- The 5-person department contains: R(White), G, B, E, and one more person.
- Clue: "H does not work with E who does not wear blue and orange."
So H is NOT in the 5-person department.
- Who is left for the 5-person department? A is in Marketing or Finance/Ops. But A wears Violet. If A is in the 5-person department, let's check D and M.
- Clue: "M neither works in finance nor with the one wearing red."
If M is not in Finance and not with Red, where is M? If M is in Operations, M could be in the 5-person department.
- Let's check which department is 5-person: Operations or Finance?
- Persons in Operations do NOT wear Black or Orange.
- T's department: T + Green.
- Red & Black department: {Red, Black}. Since Operations cannot have Black, the Red & Black department CANNOT be Operations!
- T is not in Marketing. So T is in Operations or Finance.
- If Finance is 5-person, then Operations and Marketing are 2-person departments. Then one of them is {T, Green} and the other is {Red, Black}. But Red/Black cannot be Operations, so Red/Black is Marketing, and {T, Green} is Operations!
- If Operations is {T, Green} (2 persons), then Finance is 5 persons.
- Let's verify: Clue says "The persons work in operations do not wear orange and black." This holds if Operations = {T, Green}.
- Let's check: If Operations = {T, Green}, T works ONLY with the one wearing Green. Who wears Green? D or someone else? T wears something, and the other person wears Green.
- Let's check: If Finance = 5-person department, then Finance contains R(White), G, B, E, and D/M/H/A.
- But clue: "The one wearing purple does not work in finance."
- Clue: "A does not work in operations but wears violet."
- Clue: "M neither works in finance..." -> So M CANNOT be in Finance!
- Therefore, M must be in Operations or Marketing.
- If Finance had 5 persons, M could not be in Finance. Then M must be in {T, Green} or {Red, Black}.
- If Operations is 5-person department:
- Operations = {R(White), G, B, E, M}.
- Then Finance = {T, Green} (since T is not in Marketing).
- Marketing = {Red, Black}.
- Let's test this layout:
- Operations (5 persons): R, G, B, E, M
- Finance (2 persons): T, D (or someone who wears Green)
- Marketing (2 persons): H, A (or whoever wears Red/Black)

Step 6: Assign shirts and exact persons to departments.
- Marketing (2 persons, Red & Black):
- A wears Violet, so A is not in Marketing.
- Clue: "A does not work in operations", so A must be in Finance! But Finance has T + Green. Since A wears Violet, A is NOT Green, so A CANNOT be in Finance if Finance only has 2 persons! This means A MUST be in the 5-person department!
- Therefore, Operations MUST be the 5-person department: Operations has 5 persons, Finance has 2 persons {T, Green}, Marketing has 2 persons {Red, Black}.
- Wait, A wears Violet, and A does not work in Operations. If A is in Finance, then Finance MUST be the 5-person department! Let's re-verify:
- If Finance is 5-person department: {R(White), G, B, E, A(Violet)}.
- Then M cannot work in Finance, so M is in Operations or Marketing.
- M is not with Red, so M is in Operations. Since Operations is {T, Green}, M must be T or Green! So M = T (wears something) or M wears Green.
- Then Marketing is {Red, Black}, containing H and D.
- Let's check: "H does not work with E" -> H is in Marketing, E is in Finance. Correct!
- "The one wearing purple does not work in finance." -> Purple is in Operations or Marketing.
- "G and D do not wear red and orange." -> G is in Finance, D is in Marketing (wears Black, since Red/Black are in Marketing and D doesn't wear Red, D = Black, H = Red).
- Let's check colors in Finance (5 persons: R, G, B, E, A):
- R = White
- A = Violet
- B, E, G wear remaining colors. Clue: "E does not wear blue and orange." "G does not wear orange." "Persons in operations do not wear orange and black."
- Orange must be worn by someone in Finance (since Operations has no Orange, Marketing has Red & Black). In Finance, E doesn't wear Orange, R=White, A=Violet. So B or G wears Orange. But clue: "G does not wear orange", so B wears Orange!
- What about Pink and Blue? E does not wear Blue, so G = Blue, E = Pink!
- What about Purple? "The one wearing purple does not work in finance." So Purple is in Operations (T wears Purple, M wears Green!).

Summary of initial arrangement:
- Operations (2 persons): T (Purple), M (Green)
- Finance (5 persons): R (White), G (Blue), B (Orange), E (Pink), A (Violet)
- Marketing (2 persons): H (Red), D (Black)

Step 7: Perform the requested interchange.
Question: "If M and the one wearing purple interchange their departments with E and G, then name the persons (with their shirt color) who will work in operations department?"
- Currently in Operations: M (Green) and T (Purple).
- M and T (the one wearing purple) switch places with E (Pink) and G (Blue).
- Therefore, the new persons in the Operations department are G (wearing Blue) and E (wearing Pink), which can be written as G-blue, E-pink.