Logic Masters Deutschland e.V.

The Rules:

1. [Sudoku]: Normal sudoku rules apply - fill every row, column, and 3x3 box with the digits from 1 to 9 once each.
2. [Product Killer]: Numbers in cages must not repeat and must multiply to the clue given. e.g. a cage containing 9, 9, and 25 is not allowed, but a cage containing 11, 23, and 8 is ok. Odd simply means the product must be an odd number. A, B, C, D, and E are integers that may or may not be distinct and A², B³, C², D², and E² mean those totals are perfect squares or perfect cubes. Since you cannot repeat digits, you'll have to be creative with those. (For example, 2*18 = 36 which is a square number. 3*4*18 =216 which is a perfect cube)
3. [Sandwich]: Numbers outside the grid (which must be deduced) indicate the sum of the digits in the cells sandwiched between the 1 and 9 in that row or column.

The Puzzle:

Try it on Sven's Sudokupad. Answer check is enabled for digits inside the grid.