$ javac -version
javac 11.0.12
$ java -version
openjdk version "1.8.0_222"
OpenJDK Runtime Environment (build 1.8.0_222-8u222-b10-1~deb9u1-b10)
OpenJDK 64-Bit Server VM (build 25.222-b10, mixed mode)

$ java-introcs RandomInts 24 100000 1212 | time -p java-introcs DivideImproved .
There is no solution
0: 87369 51690 14723 38833 14966 55158 17024 1096 74616 (sum: 355475)
1: 87343 79692 27312 7071 46990 1809 99176 6080 (sum: 355473)
2: 90717 27843 49949 25428 20502 90692 50344 (sum: 355475)
Best I found (not necessarily optimal): 355473 (sum: 1066423 / want: 355474 / mod 3 = 1)
real 43.68
user 43.55
sys 0.05
$ java-introcs RandomInts 24 100000 12121 | time -p java-introcs DivideImproved .
There is a solution
0: 78901 37578 47239 1864 90533 82402 92872 51853 (sum: 483242)
1: 88100 54829 39805 83279 488 82397 61783 11002 61561 (sum: 483244)
2: 39431 58314 72838 87879 97538 99482 27760 (sum: 483242)
Optimal value: 483242 (sum: 1449728 / want: 483242 / mod 3 = 2)
real 7.73
user 7.58
sys 0.05
$ java-introcs RandomInts 25 100000 12121 | time -p java-introcs DivideImproved .
There is a solution
0: 88100 39431 58314 72838 1864 97538 82402 27760 22493 (sum: 490740)
1: 78901 54829 47239 39805 83279 488 61783 11002 61561 51853 (sum: 490740)
2: 37578 82397 87879 90533 99482 92872 (sum: 490741)
Optimal value: 490740 (sum: 1472221 / want: 490740 / mod 3 = 1)
real 6.35
user 6.21
sys 0.03
$ java-introcs RandomInts 30 100000 121212 | time -p java-introcs DivideImproved .
There is a solution
0: 35085 78154 93504 6317 45784 18215 29948 18113 4130 46926 75327 (sum: 451503)
1: 79654 65492 14537 49419 20025 6581 15751 42718 80113 35293 41921 (sum: 451504)
2: 85535 89943 94459 77925 7273 78664 1852 15853 (sum: 451504)
Optimal value: 451503 (sum: 1354511 / want: 451503 / mod 3 = 2)
real 2.66
user 2.50
sys 0.03
$ java-introcs RandomInts 31 100000 121213 | time -p java-introcs DivideImproved .
There is a solution
0: 42711 36794 3675 43831 393 82991 79375 83909 59138 1459 6320 8950 36686 1268 2913 (sum: 490413)
1: 51382 55827 54428 76063 59638 91910 92445 8720 (sum: 490413)
2: 85440 63886 67107 82794 92059 44124 38598 16406 (sum: 490414)
Optimal value: 490413 (sum: 1471240 / want: 490413 / mod 3 = 1)
real 1.08
user 0.86
sys 0.08
$ java-introcs RandomInts 32 100000 121214 | time -p java-introcs DivideImproved .
There is a solution
0: 19834 93578 5867 98586 54528 45898 86522 10252 37340 46268 6985 38888 25186 (sum: 569732)
1: 97790 24494 96810 93113 7105 51836 21348 90523 86714 (sum: 569733)
2: 75695 47748 35317 67903 20486 75245 13041 72873 84606 76818 (sum: 569732)
Optimal value: 569732 (sum: 1709197 / want: 569732 / mod 3 = 1)
real 48.77
user 48.59
sys 0.05
$ java-introcs RandomInts 33 100000 121215 | time -p java-introcs DivideImproved .
There is a solution
0: 27460 35866 99685 52451 58915 31641 16641 78141 17897 32347 42795 84457 (sum: 578296)
1: 95841 96955 90809 37099 87458 6843 73057 76485 4290 9459 (sum: 578296)
2: 61340 52318 34952 47635 48622 64396 84669 6134 66222 68779 43229 (sum: 578296)
Optimal value: 578296 (sum: 1734888 / want: 578296 / mod 3 = 0)
real 15.54
user 15.33
sys 0.04