# Create a Sudoku

Write the shortest program that takes no input and outputs a Sudoku solution.

For reference, a Sudoku solution is a 9x9 grid of digits where each column, each row and each of the nine 3x3 grids that compose the board have all of the digits from 1 to 9.

Your output may look like this:

```
123456789
456789123
789123456
231564897
564897231
897231564
312645978
645978312
978312645
```

Or it may look like this:

```
123456789456789123789123456231564897564897231564897231897231564312645978645978312978312645
```

It may be an array of 9 digit integers, 3 digit integers, a 9x9 matrix or nine 3x3 matrices as well.

**You may use the digits 012345678, not 123456789**, so long as adding 1 to each digit in the output gives a valid Sudoku solution.

There used to be a script to check solutions but it doesn't work. If you code one be sure to tell me.

Your program can have multiple outputs but you'll need to prove that they are all valid solutions.

Have fun, codidactyls!

[Haskell], 50 bytes …

~1mo ago

BQN, 11 9 bytesSBCS Run onl …

~1mo ago

[APL (Dyalog Unicode)], 22 byt …

~1mo ago

Japt, 10 bytes Outputs a 2D …

~1mo ago

## 4 answers

#
BQN, ~~11~~ 9 bytes^{SBCS}

```
1⌽⍟⊢⍋3|↕9
```

The result is a length 9 list of lists using the numbers 0 to 8.

The solution is based on the 3x3 transpose list 036147258, obtained with Grade Up. This list is used to repeat the operation rotating itself by one. Since it's a self-inverse, each subsequent rotation starts it at a number one higher than the previous.

```
1⌽⍟⊢⍋3|↕9
↕9 # Range 0…8
3| # Mod 3: 012012012
⍋ # Grade: 036147258
1⌽ # Rotate by 1
⍟⊢ # Repeated n times for each number n
```

Previous solution (11): Run online!

Idea is to use the numbers 0 to 8 in order for rows and the 3x3 transpose 036147258 for columns. Adding these in a table modulo 9 gives a valid solution. Classify gets the original ordered range back from the transpose, since all its elements are unique.

```
9|+⌜⟜⊐⍋3|↕9
↕9 # Range 0…8
3| # Mod 3: 012012012
⍋ # Grade: 036147258
+⌜⟜ # Addition table with…
⊐ # Classify 012345678
9| # Modulo 9
```

#### 0 comment threads

# APL (Dyalog Unicode), 22 bytes

```
⎕←∘.((1+⍳9)⌽⍨⊣+3×⊢)⍨⍳3
```

Requires zero-indexing.

```
⎕←∘.((1+⍳9)⌽⍨⊣+3×⊢)⍨⍳3
⍳3 ⍝ Make the range [0, 2] (row and cols of 3×3 boxes)
∘. ⍨ ⍝ Outer product with itself
⊣+ ⍝ Add the row to
3×⊢ ⍝ 3 times the column
⌽ ⍝ And rotate
(1+⍳9) ⍝ The range [1,9] by that much
⎕← ⍝ Print that
```

## 2 comment threads