Failed cases found! Under Reconstruction.

See the following text files:
data_pow2to13_124
data_num_range_124
data_num_range_124II
challenge_124.out

link for CY's full codes (giving inexact solutions sometimes): ch-2.pl

# a small failed case:

$ perl ch-2.pl 1 2 3 4 9  
TOTAL: 19        
(1 3 4) ==> 8  
(2 9) ==> 11