```In this week's quiz, I ended up dropping the requirement to select or
determine puzzle difficulty. That, I suspect, is a much harder problem
than generating a quiz and also somewhat subjective. I even wondered
if anyone would attempt generating _any_ Sudoku puzzles, but _brabuhr_
presented a solution that is almost trivial. Granted, it does require
the use of a Sudoku solver (such as sudoku-x used, or perhaps one from
[quiz #43]), but I have no arguments against good reuse of code!

brabuhr begins by generating what is called the _seed puzzle_. This is
a partially-filled puzzle that should be solveable. The code for this
is:

puzzle =  * 81

a = (1..9).sort_by{rand}
b = (1..9).sort_by{rand}
c = (1..9).sort_by{rand}

# Completely fill in the upper-left 3x3 section.
puzzle[0..2] = a[0..2]
puzzle[9..11] = a[3..5]
puzzle[18..20] = a[6..8]

# Completely fill in the center 3x3 section.
puzzle[30..32] = b[0..2]
puzzle[39..41] = b[3..5]
puzzle[48..50] = b[6..8]

# Completely fill in the lower-right 3x3 section.
puzzle[60..62] = c[0..2]
puzzle[69..71] = c[3..5]
puzzle[78..80] = c[6..8]

I added in a few comments to show what parts of the 9x9 puzzle are
being modified. As the upper-left, central, and lower-right 3x3
sections are completely independent of one another, they can be filled
at random without any expection of contradiction (assuming the rest of
the puzzle is still empty, ensured here by the initial fill of zero).

Visually, the seed puzzle will look something like this (zeros have
been replaced with blanks to improve clarity):

+-------+-------+-------+
| 6 8 5 |       |       |
| 3 1 9 |       |       |
| 7 2 4 |       |       |
+-------+-------+-------+
|       | 2 1 8 |       |
|       | 4 5 6 |       |
|       | 9 7 3 |       |
+-------+-------+-------+
|       |       | 2 1 8 |
|       |       | 4 5 6 |
|       |       | 9 7 3 |
+-------+-------+-------+

The next step is to generate the rest of the puzzle. But since this is
exactly what a solver does, brabuhr uses a solver to generate the
puzzle.

puzzle = solve(puzzle)

I'm not sure whether or not the seed has multiple solutions, but it
doesn't really matter. This is just the first part of creating a
puzzle for humans to solve, so as long as the solving library provides
_some_ solution, we'll have a usable puzzle.

The final step is to take the "solved" puzzle and poke holes in it,
enough so we have a real puzzle for humans to solve. Again, this is
quite simple:

64.times{puzzle[rand(81)] = 0}

This line will punch at most 64 holes into the puzzle. 64 is chosen as
the upper limit, since there seems to be some evidence that the
[Minimum Sudokus] -- puzzles uniquely solveable with the least
number of clues -- seems to require 17 clues (and 81 - 17 = 64). It is
quite likely, however, that there will be some overlap in the hole
choices, and so there will likely be more than 17 clues: fewer holes
means more clues, which means (generally) an easier puzzle.

So it is certainly possible that this generator will create puzzles
with more than one solution. _Kaz Kylheku_ provided a suggestion to
deal with that:

An obvious way to improve your generator would be to call the
solver function
after punching a hole. (The solver function hopefully tells you
that the
puzzle has two or more solutions, right?) If after punching a
hole, the puzzle
has more than one solution, then backtrack; restore the hole, and
punch out a
different number.

: http://rubyquiz.com/quiz43.html
: http://people.csse.uwa.edu.au/gordon/sudokumin.php

```