Logic Masters Deutschland e.V.

This puzzle has been constructed as a preparation puzzle for this year's German Sudoku Championship.

Rules: Put a number in each cell, such that in every row, column and area, the numbers from 1 to 9 appear exactly once. In every grey cell there starts a orthogonal (horizontal or vertical) path that goes through all the numbers down to 1 in descending order. All possible grey cells are given. Cells containing a 1 are not grey.