Logic Masters Deutschland e.V.

This puzzle was inspired by Justalilguy, who has already presented something similar – although considerably larger and more beautiful. I therefore wanted to try my hand at a small puzzle of this type. I hope this puzzle genre has not been patented; if it has, please let me know and I will, of course, delete the puzzle.

Japanese Sums: Shade some cells inside the grid and fill the remaining cells with digits from 1 to 9. Digits may not repeat in any row or column. The clues to the left of each row give the sums of its contiguous unshaded blocks from left to right; the clues above each column give them from top to bottom. Consecutive blocks are separated by at least one shaded cell.

All shown cells outside the grid are clue cells. They always contain a non-zero clue value and can never be shaded. Only some exact clue values are given. A large number shown in a clue cell is its exact value, while an empty clue cell has an entirely unknown value. ? represents a single-digit clue and ?? a two-digit clue. A clue range such as 2–9 allows any integer clue value from 2 to 9, inclusive.

Ranked Cages: The small number in a dashed cage gives the rank of its sum among all 13 cage sums. Cage 1 has the smallest sum and cage 13 the largest; all cage sums are different. Shaded grid cells contribute 0 to the cage sum, and multiple shaded cells may occur in the same cage. Digits in unshaded grid cells may not repeat within a cage.

Cages may also contain clue cells outside the grid. Their actual clue values contribute to the cage sum. Yellow cells, both inside and outside the grid, belong to no cage. Yellow cells inside the grid otherwise follow the normal Japanese Sums rules.

For two adjacent cells separated by an inequality sign, the indicated inequality applies. Both cells must contain numbers and cannot be shaded. This applies both inside the grid and to clue cells outside the grid.