Six friends P, Q, R, S, T and U play six different games and belong to six…

Concept: This is a two-attribute matching puzzle — six people must each be paired with one city AND one game. The standard method is to build a grid, enter every directly-stated fact first, then repeatedly apply the remaining clues to eliminate impossible pairings until every row has a unique city and game.

Application — filling the grid step by step:

1. Enter the directly-stated facts: P is Lucknow/Hockey, U plays Basketball, S is Delhi (and not Badminton), T is Kolkata.

2. The three remaining cities — Kanpur, Bangalore, Agra — must belong to Q, R and U in some order.

3. The Kanpur resident plays Football and is explicitly not R. U already plays Basketball, so U cannot also be the Football-playing Kanpur resident. That leaves Q as the only person who can be from Kanpur, so Q is from Kanpur and plays Football.

4. Bangalore and Agra remain for R and U. The Cricket player is from Bangalore; U plays Basketball, not Cricket, so U cannot be from Bangalore. Hence R is from Bangalore and plays Cricket, and U is from Agra.

5. Badminton and Golf remain for S and T. S does not play Badminton, so S plays Golf and T plays Badminton.

Cross-check: every one of the six original clues holds against this completed grid (P-Hockey-Lucknow, U-Basketball, Kanpur-Football-not R, S-Delhi-not Badminton, Cricket-Bangalore, T-Kolkata), confirming the grid is consistent and unique.

Result: Q plays Football.