Workshop › Sudoku › Step 21 of 28

Invent a puzzle

What we are doing

Now the computer invents puzzles: make a random full grid, then empty cells in random order. After each removal, check with the solver that the puzzle still has exactly one solution; if not, put the digit back.

```js
const HOLES = 50 // how many cells are emptied

const copy = (board) => board.map((row) => row.slice())

// A random full grid, then empty cells one by one, keeping only removals that leave exactly one solution.
function makePuzzle() {
  const full = Array.from({ length: 9 }, () => Array(9).fill(0))
  countSolutions(full, 1, true)
  const puzzle = copy(full)
  let removed = 0
  for (const cell of shuffle([...Array(81).keys()])) {
    if (removed === HOLES) break
    const r = Math.floor(cell / 9)
    const c = cell % 9
    const digit = puzzle[r][c]
    puzzle[r][c] = 0
    if (countSolutions(copy(puzzle), 2) === 1) removed++
    else puzzle[r][c] = digit // two solutions: put it back
  }
  return { puzzle, full }
}
```

What it means

• copy makes a new grid with the same digits, so the solver can scribble on it without spoiling the puzzle.
• [...Array(81).keys()] is the list 0 to 80, one number per cell; shuffled, it is a random order of cells.
• Cell number n is row Math.floor(n / 9), column n % 9.
• Counting up to 2 is enough: 1 means unique, 2 means "more than one".

Your turn

1. Under TOP, write HOLES.
2. Under shuffle, write copy, the comment and makePuzzle.

Skills: Functions, Loops

← Random order A new puzzle every game →

All steps

1. Nine by nine
2. Lines and boxes
3. A puzzle from a string
4. The puzzle's own digits
5. Keep drawing
6. The selected cell
7. Light up row, column and box
8. The same digit everywhere
9. Click to select
10. Move with the arrows
11. Write digits
12. The three rules in one loop
13. Show mistakes
14. Solved!
15. A clock
16. The solved message
17. Play again
18. The easiest cell
19. The solver
20. Random order
21. Invent a puzzle
22. A new puzzle every game
23. Hints
24. Best time
25. N for a new puzzle
26. A number pad
27. Tap the pad
28. Build it yourself: undo