It's because he's a pupil. Pupils clean in Japan. In vol 1 Hikaru attacks some students with a mop (http://www.onemanga.com/Hikaru_no_Go/13/04/); it's no mere chance he has that mop, he's been cleaning the bathrooms with it. And it's not detention either; it's normal in Japan for the students to clean the school.
And for the pupils to help with the dishes.