Build a Killer Sudoku Solver
GolfScript, 138 characters
n%~[~]:N;1/:P.&amp;:L;9..*?{(.[{.9%)\9/}81*;]:§;L{.`{\~@@=*}+[P§]zip%{+}*\L?N==}%§9/..zip+\3/{{3/}%zip{{+}*}%}%{+}*+{.&amp;,9=}%+1-,!{§puts}*.}do;

This is a killer sudoku solver in GolfScript. It expects input on STDIN in two rows as given in the example above.
Please note: Since the puzzle description does not make any restrictions on execution time I preferred small code size over speed. The code tests all 9^81 grid configurations for a solution which may take some time on a slow computer ;-)