TSQL Select random rows WITH running total - tsql

Question

TSQL, I am using SQL 2012 but will use anything that works from previous versions. I know how to select TOP X random rows from a table using NEWID(). Separately, I know how to select a running total using several methods, CTE, etc.
BUT, how would one combine these 2 results into one query? So I want to select say 3 random records (AND no less than 3), where the running total does not exceed 15. Can't wrap my head around this one...
Use this simple table and data:
CREATE TABLE TblTest (
id int not null identity(1,1) primary key,
value int not null
);
INSERT INTO TblTest (value) VALUES (4);
INSERT INTO TblTest (value) VALUES (3);
INSERT INTO TblTest (value) VALUES (5);
INSERT INTO TblTest (value) VALUES (6);
INSERT INTO TblTest (value) VALUES (6);
INSERT INTO TblTest (value) VALUES (5);
INSERT INTO TblTest (value) VALUES (6);
INSERT INTO TblTest (value) VALUES (5);
INSERT INTO TblTest (value) VALUES (4);
INSERT INTO TblTest (value) VALUES (7);
INSERT INTO TblTest (value) VALUES (7);
INSERT INTO TblTest (value) VALUES (6);
INSERT INTO TblTest (value) VALUES (5);
INSERT INTO TblTest (value) VALUES (4);
My Attempt is below, not sure if it even makes sense having the NEWID there, and sometimes it returns only 2 rows, sometimes 0, I want it to be smart enough to return always 3 rows, and if possible, closest to 15...:
select top(3) ourRandID,
id,
value,
running_total
from (
select NEWID() as ourRandID,
id,
value,
sum(value) over (order by NEWID()) as running_total
from TblTest
) t
where running_total < 16

Answer 1

try this:
select t.*
from TblTest t
join
(
select top (1)
t1.id [id1],t2.id [id2],t3.id [id3],
t1.value[v1],t2.value [v2],t3.value [v3],
t1.value+t2.value+t3.value [sum]
from TblTest t1
join TblTest t2 on (t1.id <> t2.id)
join TblTest t3 on (t3.id <> t2.id and t3.id <> t1.id)
where t1.value+t2.value+t3.value <= 15
order by t1.value+t2.value+t3.value desc,newid()
) [a] on (t.id=a.id1 or t.id=a.id2 or t.id=a.id3)