Can someone explain the logic to this puzzle (the killer one).

http://www.timesonline.co.uk/article/0,,18209-1769363,00.html

I understand that 1-5 are in c5 r3-r7 so

r2c5 has to be 6 r2c6 has to be 1

r8c5has to be 7 r8c4 has to be 1

and 16 in row 5 has to be 7 and 9

and r1c5 can be 8 or 9

and r9c5 can be 8 or 9

r1c3 has to be 1 cause you either have 3 or 4 left to make 12

I finished this puzzle but only by trial and error.... well actually after messing up about 5 tiimes I just looked what numbers I had on all 5 papers and started with them. This seemed way harder than even the 'deadly' example sudoku.

thanks for any help