Five friends, Purva, Roshan, Vibhor, Luna and Anuj, are wearing five different coloured T-shirts, red, black, purple, yellow and blue. Each of the friends is allergic to one of the following: nuts, dairy, cats, fish and dust, such that no two has the same allergy. Luna is allergic to cats but is not wearing a purple T-shirt. The one wearing a yellow T-shirt has dust allergy. Purva is wearing a black t-shirt but is not allergic to dairy or fish. Vibhor is wearing a purple T-shirt but does not have fish allergy. Luna is wearing a blue T-shirt. Roshan is wearing a red T-shirt. Who is allergic to dust?
Logic Puzzle Deduction
This problem requires matching five friends, their T-shirt colors, and their allergies using a set of clues.
Key Information and Clues
- Friends: Purva, Roshan, Vibhor, Luna, Anuj
- T-shirt Colors: Red, Black, Purple, Yellow, Blue
- Allergies: Nuts, Dairy, Cats, Fish, Dust
Provided Clues:
- Luna is allergic to cats but is not wearing a purple T-shirt.
- The person wearing a yellow T-shirt has a dust allergy.
- Purva is wearing a black T-shirt and is not allergic to dairy or fish.
- Vibhor is wearing a purple T-shirt and does not have a fish allergy.
- Luna is wearing a blue T-shirt.
- Roshan is wearing a red T-shirt.
Step-by-Step Solution
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Assign Known T-shirt Colors:
- Luna wears Blue (Clue 5).
- Roshan wears Red (Clue 6).
- Vibhor wears Purple (Clue 4).
- Purva wears Black (Clue 3).
The only remaining friend is Anuj, and the only remaining color is Yellow. Therefore, Anuj wears the Yellow T-shirt.
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Assign Known Allergies:
- Luna is allergic to Cats (Clue 1).
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Identify Dust Allergy:
According to Clue 2, the person wearing the Yellow T-shirt has a dust allergy. Since Anuj wears the Yellow T-shirt, Anuj is allergic to dust.
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Complete Remaining Assignments (Verification):
- Purva (Black T-shirt): Not allergic to Dairy or Fish (Clue 3). The only remaining allergy is Nuts. Purva is allergic to Nuts.
- Vibhor (Purple T-shirt): Not allergic to Fish (Clue 4). The only remaining allergy is Dairy. Vibhor is allergic to Dairy.
- Roshan (Red T-shirt): The only remaining allergy is Fish. Roshan is allergic to Fish.
Final Mapping Summary
| Friend | T-shirt Color | Allergy |
| Purva | Black | Nuts |
| Roshan | Red | Fish |
| Vibhor | Purple | Dairy |
| Luna | Blue | Cats |
| Anuj | Yellow | Dust |
Dust Allergy Conclusion
Following the logical deductions from the clues, Anuj is identified as the friend who is allergic to dust.
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