# Sudoku with no grid and no numbers!!? - SS#12

An entry in Fortnightly Topic Challenge #47: "Wacky Sudokus"

Other puzzles in this series

Welcome to the twelfth puzzle in this series! For more information about the series, see the first puzzle and the introduction. Enjoy!

I got bored of giving you actual clues, so here are some fake ones

RULES:

• Normal Sudoku rules apply
• However, there are no boxes in this grid, just rows and columns
• The numbers given are incorrect, the actual entry is either one more or one less than the given number

Only three left! Hopefully everyone has enjoyed so far, there are still 2 more to be released in the next 2 days which are quite interesting ones. Good luck!

• Alright so since the boxes are missing, we only need to fill this sudoku given the condition that all the rows and columns only have each number from 1 to 9, am I right? Commented Jan 21, 2021 at 17:46
• @Anonymous correct, only the rows and columns need that Commented Jan 21, 2021 at 18:01

COMPLETED GRID

REASONING

To begin:

Any pseudo-clues that are 1s or 9s must actually be 2s and 8s, respectively. Then any 3s in a row/column with an actual 2, and 7s in a row/column with an actual 8, must resolve to 4s and 6s, respectively. Then we can repeat with existing clues to see what's forced, and in fact we're able to fill in almost all of the odd pseudoclues in this manner. The grid at this stage:

A deduction:

In the top row, the two pseudo-4s must resolve to 3 and 5 respectively, forcing the 2 in that row to resolve to a 1. The exact same situation occurs in row 6. Similar logic in row 8 forces the 6 pseudoclue there to resolve to 5. We can then chase the implications of this to get almost all the remaining clues. The grid thus far: