Workshop › Sudoku › Step 20 of 28

Random order

What we are doing

Solving an empty board gives a full, valid Sudoku grid, but always the same one. Shuffling the options makes the solver build a different random grid every time. This is the first half of inventing puzzles.

```js
// Counts solutions up to `limit`; `order` shuffles the digits to make random grids.
function countSolutions(board, limit = 2, order = false) {
  const cell = bestCell(board)
  if (!cell) return 1 // no empty cell left: solved
  const { r, c, options } = cell
  if (order) shuffle(options)
  let count = 0
  for (const d of options) {
    board[r][c] = d
    count += countSolutions(board, limit - count, order)
    if (count >= limit) return count // keep the board as it is: that is the solution
    board[r][c] = 0
  }
  return count
}

function shuffle(list) {
  for (let i = list.length - 1; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1))
    ;[list[i], list[j]] = [list[j], list[i]]
  }
  return list
}
```

What it means

• order defaults to false, so solving works as before; with true the options are shuffled first, all the way down.
• Fisher–Yates: from the end, swap each item with a random one at or before it. Every order is equally likely.
• [a, b] = [b, a] swaps two values. The ; at the start keeps JavaScript from gluing the line to the one before.

Your turn

1. Change the second comment line and the function's first line to add order.
2. Shuffle the options when order is on, and pass order along in the recursive call.
3. Under countSolutions, write shuffle.

Skills: Arrays and objects

← The solver Invent a puzzle →

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