Zero Cages
(Published on 9. July 2022, 19:36 by Bonehead)
My first puzzle on here, inspired by an idea I had related to using negative numbers.
Rules.
Sudoku rules apply except in cages where the numbers -9 to -1 can also appear. For purposes of sudoku (rows, columns, boxes and cages) negative numbers count as positive ones (eg a cage, row etc. cannot contain both a -1 and a 1).
In cages,the cells total to zero, digits do not repeat and the number indicated in the cage is the difference between the lowest and highest digits in that cage, with the lowest digit also in the numbered cell, ascending in order to the highest digit. Where this is not possible (the next digit has a choice of 2 or more cells) the remaining digit order must be determined and the ascending order rule is to be ignored. EG: If a horizontal 4 cell cage indicator is 10 and is at left of the cage a possible solution is -6,-1,3,4. If the 10 was in the second to left cell of the cage all that can initially be determined is ?,-6,?,?.
The round circle indicates a difference of 1 between cells.
The square indicates a valid squared relationship between cells, ie. one number is the square of the other.
Two of the cages are liars and must be completely ignored.
Penpa+ version to try here
Full solution here
Happy solving
Solution code: Row5, Column 9, enter negative numbers as -x (no gaps)
Comments
on 12. July 2022, 18:38 by Bonehead
Improved description to clarify 1 point. The 16 cell is valid as per rules I meant, but DiMono was correct in saying this wasn’t 100% clear.
Newby mistake I won’t make again. :)
on 12. July 2022, 18:16 by Bonehead
DiMono pointed out I had mistyped the original descriptions -8,3,5 clue example as -8,5,3. Apologies, not sure where my brain went when typing that but updated to be clearer with a 4 cell example.
on 12. July 2022, 04:35 by DiMono
The example of digit order you gave does not match the description of the rule. If the digits need to ascend in value, then -8,5,3 would be invalid because the largest digit is 5. The valid order would be -8,3,5 as -8 < 3 < 5. I think either the example is wrong, or the explanation is incorrect.
