Who belongs to Jaipur?
Deduction Steps for City Assignment
This logic puzzle requires us to assign each of the seven friends (P, Q, R, S, T, U, V) to one of the seven cities (Shimla, Manali, Agra, Jaipur, Goa, Guwahati, Darjeeling) based on the given clues.
Initial Clue Mapping
We start by listing the direct assignments and constraints:
- T belongs to Darjeeling.
- S belongs to Manali.
- V belongs to Shimla.
- Q belongs to Agra.
- Either R or U belongs to Guwahati.
- P does not belong to Goa.
Tracking Assignments
Let's use a table to track the assignments and remaining possibilities:
| Friend | City Assigned | Notes/Constraints |
|---|---|---|
| T | Darjeeling | Given |
| S | Manali | Given |
| V | Shimla | Given |
| Q | Agra | Given |
| P | ? | Cannot be Goa. Needs assignment. |
| R | ? | Either Guwahati or remaining city. |
| U | ? | Either Guwahati or remaining city. |
Identifying Remaining Cities and People
The cities already assigned are Darjeeling, Manali, Shimla, and Agra. The remaining cities are Jaipur, Goa, and Guwahati.
The friends without assigned cities are P, R, and U.
Applying Constraints for R and U
We know that one of R or U must be in Guwahati. This leaves two possibilities for the assignments of P, R, and U to Jaipur, Goa, and Guwahati:
- Case 1: R is in Guwahati.
- Case 2: U is in Guwahati.
Case 1: R is in Guwahati
If R is in Guwahati, then U cannot be in Guwahati. The remaining cities for P and U are Jaipur and Goa.
Since P cannot be in Goa, P must be assigned to Jaipur.
This leaves U to be assigned to Goa.
Assignments in Case 1: P=Jaipur, Q=Agra, R=Guwahati, S=Manali, T=Darjeeling, U=Goa, V=Shimla.
Case 2: U is in Guwahati
If U is in Guwahati, then R cannot be in Guwahati. The remaining cities for P and R are Jaipur and Goa.
Again, since P cannot be in Goa, P must be assigned to Jaipur.
This leaves R to be assigned to Goa.
Assignments in Case 2: P=Jaipur, Q=Agra, R=Goa, S=Manali, T=Darjeeling, U=Guwahati, V=Shimla.
Final Conclusion
In both possible scenarios derived from the clues, P is assigned to Jaipur. Therefore, P belongs to Jaipur.
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