SQL Update query with group by clause

Name         type       Age
-------------------------------
Vijay          1        23
Kumar          2        26
Anand          3        29
Raju           2        23
Babu           1        21
Muthu          3        27
--------------------------------------

Write a query to update the name of maximum age person in each type into 'HIGH'.

And also please tell me, why the following query is not working

update table1 set name='HIGH' having age = max(age) group by type;

I have changed the script from Derek and it works for me now:

UPDATE table1 AS t 
INNER JOIN 
(SELECT type,max(age) mage FROM table1 GROUP BY type) t1 
ON t.type = t1.type AND t.age = t1.mage 
SET name='HIGH'

You can't use group by directly in an update statement. It'll have to look more like this:

update t
set name='HIGH'
from table1 t
inner join (select type,max(age) mage from table1 group by type) t1
on t.type = t1.type and t.age = t1.mage;

Since I looked-up this response and found it a little bit confusing to read, I experimented to confirm that the following query does work, confirming Svetlana's highly-upvoted original post:

update archives_forum f
inner join ( select forum_id, 
    min(earliest_post) as earliest, 
    max(earliest_post) as latest 
  from archives_topic 
    group by forum_id 
  ) t 
  on (t.forum_id = f.id)
set f.earliest_post = t.earliest, f.latest_post = t.latest;

Now you know ... and so do I.