Logic Masters Deutschland e.V.

This is my second puzzle, it is a follow-up to Mod Prod in the Fog, which I published about a year ago, and is solved in this video.

Click the image below to play the puzzle on SudokuPad.

Rules: Normal sudoku rules apply.

Each letter found in this puzzle (A, B, C, etc) represents a different digit (1-9), with values to be determined by the solver.

All multiplication is performed modulo 10, which means we only keep the last digit of a product. For example: 3*4=2.

A value placed outside the 9x9 grid indicates an x-product for that row/column. This is like an x-sum but for multiplication. For example, if a K is placed above a column, and the first digit in that column is N, then the first N digits in that column (including the N) multiply to K.

Digits in a cage multiply to the small value given in the corner of one of its cells.

Dynamic fog: placing a correct digit will clear the fog in that cell and sometimes other cells too. Guessing is never necessary and always a bad idea.

Math hints: Remember that multiplication modulo 10 is associative: you will only need your 9 times tables for this puzzle. Also, you can do a kind of "division modulo 10" which is not as hard as it sounds, and you can absolutely figure out on your own.