For a puzzle with a difference which requires both logic and multiplication try a Find the Factors puzzle from Iva Sallay on her Find the Factors blog. In this Find the Factors 1-10 puzzle can you place the numbers 1 to 10 in the first row and the first column to make the multiplication table work? Iva Sallay has clearly explained the puzzles here: How to Find the Factors.
New puzzles are published each week, I like the Excel files provided with puzzles of varying levels of difficulty. You will also find many hints and tips in the various posts. See Hooked on Factoring, for example, a post giving techniques for solving the puzzles and an Excel file of puzzles.