Normal sudoku rules apply. Furthermore there are 3 snakes hidden in the grid. Each snake is a set of cells sharing an edge or a corner; each snake cannot branch; touch itself (orthogonally or diagonally) or touch another snake (orthogonally or diagonally). Each snake's cells contain digits which, when multiplied together, give exactly 500. Parts of some or all the snakes are shown as grey lines in the grid. No snake can start or end in the digit 1. NB as cells on the same snake cannot touch diagonally r2c4, for example, in this puzzle cannot be snake (as the snake cell r3c3 touches r2c4 diagonally).