The triangular numbers up to and immediately beyond 24 are
1 = 1
1+2 = 3
1+2+3 = 6
1+2+3+4 = 10
1+2+3+4+5 = 15
1+2+3+4+5+6 = 21
1+2+3+4+5+6+7 = 28
So, of these, only 3 + 21 can be added together to make 24
34
34
17 and 7
-22
199
20
11 and 13
34
-101
34
14
1
-22
17 and 7
-29
13
-676