Re: "the World's hardest logic/number puzzles"
After finding some extra time I have solved your nr. 7
"The Hardest Kakuro Puzzle" (originally from Conceptis Puzzles). This Kakuro is quite difficult (it requires some previous experience in Kakuros) and, in my opinion, it requires more time than, for instance, the "Hardest Killer Sudoku" (I mean the 21/12/2012 from killersudokuonline and not the nr. 3 of the paper
as already commented).