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db<>fiddle
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CREATE TABLE mytable(
id VARCHAR(34) NOT NULL PRIMARY KEY
,room_id INTEGER
,seat_num VARCHAR(6)
);
INSERT INTO mytable(id,room_id,seat_num) VALUES ('1',1,NULL);
INSERT INTO mytable(id,room_id,seat_num) VALUES ('2',1,NULL);
INSERT INTO mytable(id,room_id,seat_num) VALUES ('3',2,NULL);
INSERT INTO mytable(id,room_id,seat_num) VALUES ('4',2,NULL);

update mytable t
inner join (
select id, (select count(*) from mytable t1 where t1.room_id = t.room_id and t1.id <= t.id) rn
from mytable t
) t1 on t1.id = t.id
set t.seat_num = t1.rn
Rows matched: 4  Changed: 4  Warnings: 0
select * from mytable
id room_id seat_num
1 1 1
2 1 2
3 2 1
4 2 2