First of all, you did not yet specify what should happen if two or more rows within the same day contain an equal high score.
Two possible answers to that question:
1) Just select one of the scoredatetime's, it doesn't matter which one
In this case don't use self joins or analytics as you see in the other answers, because there is a special aggregate function that can do your job more efficient. An example:
SQL> create table mytable (scoredatetime,score)
2 as
3 select to_date('01-jan-2009 00:10:00','dd-mon-yyyy hh24:mi:ss'), 10 from dual union all
4 select to_date('01-jan-2009 01:00:00','dd-mon-yyyy hh24:mi:ss'), 11 from dual union all
5 select to_date('01-jan-2009 04:00:00','dd-mon-yyyy hh24:mi:ss'), 9 from dual union all
6 select to_date('02-jan-2009 00:10:00','dd-mon-yyyy hh24:mi:ss'), 1 from dual union all
7 select to_date('02-jan-2009 01:00:00','dd-mon-yyyy hh24:mi:ss'), 1 from dual union all
8 select to_date('02-jan-2009 04:00:00','dd-mon-yyyy hh24:mi:ss'), 0 from dual
9 /
Table created.
SQL> select max(scoredatetime) keep (dense_rank last order by score) scoredatetime
2 , max(score)
3 from mytable
4 group by trunc(scoredatetime,'dd')
5 /
SCOREDATETIME MAX(SCORE)
------------------- ----------
01-01-2009 01:00:00 11
02-01-2009 01:00:00 1
2 rows selected.
2) Select all records with the maximum score.
In this case you need analytics with a RANK or DENSE_RANK function. An example:
SQL> select scoredatetime
2 , score
3 from ( select scoredatetime
4 , score
5 , rank() over (partition by trunc(scoredatetime,'dd') order by score desc) rnk
6 from mytable
7 )
8 where rnk = 1
9 /
SCOREDATETIME SCORE
------------------- ----------
01-01-2009 01:00:00 11
02-01-2009 00:10:00 1
02-01-2009 01:00:00 1
3 rows selected.
Regards,
Rob.