Normal sudoku rules apply. Numbers outside the grid (including those on lines extending outside the grid) are X-Sums, which sum the first X digits from the clue, where X is the first digit seen. Along the grey thermos, values must increase from the bulb end. Along the pink renban lines, values must form a non-repeating consecutive sequence in any order. Along the blue region sum lines values have an equal sum N within each box they pass through. Different lines may have different values of N. Values in cages sum to the given clue.