Rules:
Cartesian Sums: For each cell in the grid consider its coordinates as shown in grey outside the grid. Shade some of the cells of the grid and write in each unshaded cell the sum of its coordinates (e.g. the cell in the coordinates [3,-5] would contain the number -2). Shaded cells cannot contain numbers.
The clues outside the grid are Japanese Sum clues. A number indicates the absolute value of the sum of the digits in a consecutive set of unshaded cells. Such sets are separated by at least one shaded cell. The clues are given in the right order and every consecutive set of unshaded cells is accounted for by Japanese Sum clues.
A single '?' represents an absolute value from 0 to 9. A '??' represents an absolute value between 10 and 99, i.e. the leading digit can't be 0. E.g. '1?' could be any number from 10 to 19 and '?4' can be 14, 24, 34, etc. A '*' represents any number of sets of consecutive unshaded cells with arbitrary sums including no unshaded cells at all.
Draw a non-intersecting, non-branching loop through the centers of all unshaded cells.
Furthermore, the grid is divided in four quadrants. In each quadrant, there is a single and distinct clue type that appears only within the boundaries of that quadrant and interacts only with the cells of its quadrant and inside the borders of its quadrant. The clue types and relative rules are as follows:
Solution code: Column -3, from top to bottom (16 letters): put the letter X for a shaded cell, the letter T for a turn of the loop and the letter S for a straight piece of the loop. Es. XXXTTTTSSTSXXSSX
on 30. December 2025, 11:46 by Nensche777
This was really fun, thanks! Looking forward to possibly more puzzles of this type!
on 13. December 2025, 18:31 by yttrio
Very cool logic from the Cartesian sums idea, and I'm always a sucker for a good loop puzzle!
on 12. December 2025, 22:47 by dumediat
I really loved this idea, and the use of the absolute values of cells turned what could have been a tedious solve into a really smooth and enjoyable one!
on 8. December 2025, 12:47 by Playmaker6174
Very original concept and a great fun (and surprisingly not too tricky) solve here! I’m a sucker for some funny arithmetic works there x)
on 3. December 2025, 16:40 by Agent
Cool concept and great execution!
on 3. December 2025, 07:05 by Christounet
Original idea and very funny how this works! Thanks :)
on 3. December 2025, 00:01 by sfushidahardy
Fun puzzle!