#
Off-by-One Error

A computer wrote these logic puzzles, but they’re all a little bit wrong. All given numbers in every odd column and every odd row *might be* shifted up by 1.

For example, when I generated a mini-sudoku, I received this invalid puzzle:

The givens in Row 3, Column 1 and Column 5 were shifted. What I was meant to see was:

### Skyscraper

- A number between 1 and 9 (inclusive) must appear in each cell
- Each row and column must be full of unique numbers
- Numbers in each cell represents the “height” of a skyscraper in that cell
- The number on either side of each row and column represents how many skyscrapers one would see from that vantage point, where taller skyscrapers block the view of shorter skyscrapers
- E.g. If the numbers in the first row were “3 5 4 1 2”, the number on the left side would be 2 (because one would see skyscrapers of height 3 and 5), and the number on the right side would be 3 (because one would see skyscrapers of height 2, 4, and 5)

| 8 | 9 | 8 | 3 | 6 | 4 | 6 | 2 | 1 | |

4 | | | | | | | | | | 1 |

3 | | | | | | | | | | 2 |

3 | | | | | | | | | | 5 |

3 | | | | | | | | | | 3 |

4 | | | | | | | | | | 3 |

2 | | | | | | | | | | 2 |

2 | | | | | | | | | | 4 |

3 | | | | | | | | | | 2 |

3 | | | | | | | | | | 3 |

| 3 | 1 | 2 | 2 | 2 | 2 | 3 | 2 | 2 | |

| 8 | 5 | 1 | 5 | 6 | 4 | 3 | 3 | 8 | |

3 | | | | | | | | | | 4 |

4 | | | | | | | | | | 3 |

5 | | | | | | | | | | 3 |

3 | | | | | | | | | | 2 |

2 | | | | | | | | | | 3 |

2 | | | | | | | | | | 4 |

3 | | | | | | | | | | 3 |

2 | | | | | | | | | | 1 |

2 | | | | | | | | | | 6 |

| 1 | 2 | 2 | 3 | 2 | 2 | 3 | 2 | 3 | |

### Killer Sudoku

- A number between 1 and 9 (inclusive) must appear in each cell
- Each row, column, and nonet must be full of unique numbers
- The grid is separated into “cages”
- The numbers inside cages must sum to the number written in its top-left corner
- Cages contain unique numbers

Grayscale image

19 | | | 17 | | 13 | | | 10 |

14 | | 12 | | 16 | | 14 | | |

14 | | | 15 | | 7 | | | 18 |

| 5 | | | 10 | | 13 | | |

| 14 | | 18 | | | 15 | | |

10 | 5 | 12 | 8 | | 16 | | 5 | 17 |

| | | 12 | 8 | | 15 | | |

24 | | 8 | | | | | 16 | |

| | | 14 | | 4 | | | |

Grayscale image17 | | 11 | 12 | | 17 | | 13 | |

23 | | | | | 5 | 10 | | 14 |

| | 4 | 14 | | | | | |

7 | | | 15 | 7 | | 18 | | 7 |

13 | | 24 | | 19 | | | | |

| | | 7 | | 14 | 14 | 13 | 15 |

11 | | 15 | | | | | | |

8 | | | 13 | | | 8 | | |

15 | | | 13 | | 21 | | | |

### Shikaku

- Board must be divided into rectangles
- Exactly 1 number must be inside each rectangle
- The area of each rectangle must be equal to the number inside it

### Slitherlink

- If a cell contains a number, the amount of lines around the cell must be equal to it
- Lines may not branch (i.e. create a T-shape) nor intersect (i.e. create a plus-shape)
- Line must form a single continuous loop

4 | 2 | | | 3 | 1 | | | 4 |

| | 1 | 1 | 4 | | | 1 | 1 |

1 | | 2 | 2 | | | 3 | | |

2 | 3 | | | 2 | 0 | 4 | 2 | |

| | 1 | | 3 | | | 1 | 2 |

| | | | 3 | 1 | 2 | | |

3 | 3 | 3 | | | | | 4 | |

2 | | 1 | 1 | | 1 | | 3 | |

1 | | 3 | 2 | 3 | 3 | | 3 | 4 |

| 3 | | 2 | 2 | 1 | 2 | 3 | |

1 | | | 3 | | 1 | | | 2 |

2 | 3 | | | 2 | | 3 | 2 | |

2 | | 2 | | | 2 | 1 | | 2 |

| 3 | | 1 | 1 | | 1 | 2 | |

1 | | 3 | 0 | | 3 | | | |

1 | 0 | | 2 | 1 | | 1 | | 3 |

| 1 | 1 | | | 2 | 1 | 2 | |

| 2 | | 3 | | 2 | | 3 | 3 |