Sudoku
use v6;
my @A = <
5 3 0 0 2 4 7 0 0
0 0 2 0 0 0 8 0 0
1 0 0 7 0 3 9 0 2
0 0 8 0 7 2 0 4 9
0 2 0 9 8 0 0 7 0
7 9 0 0 0 0 0 8 0
0 0 0 0 3 0 5 0 6
9 6 0 0 1 0 3 0 0
0 5 0 6 9 0 0 1 0
>;
my &I = * div 9; # line number
my &J = * % 9; # column number
my &K = { ($_ div 27) * 3 + $_ % 9 div 3 }; # bloc number
sub solve {
for ^@A -> $i {
next if @A[$i];
my @taken-values = @A[
grep {
I($_) == I($i) || J($_) == J($i) || K($_) == K($i)
}, ^@A
];
for grep none(@taken-values), 1..9 {
@A[$i] = $_;
solve;
}
return @A[$i] = 0;
}
my $i = 1;
for ^@A {
print "@A[$_] ";
print " " if $i %% 3;
print "\n" if $i %% 9;
print "\n" if $i++ %% 27;
}
}
solve;
Output:
5 3 9 8 2 4 7 6 1
6 7 2 1 5 9 8 3 4
1 8 4 7 6 3 9 5 2
3 1 8 5 7 2 6 4 9
4 2 5 9 8 6 1 7 3
7 9 6 3 4 1 2 8 5
8 4 1 2 3 7 5 9 6
9 6 7 4 1 5 3 2 8
2 5 3 6 9 8 4 1 7
This is an alternative solution that uses a more ellaborate set of choices instead of brute-forcing it.
#!/usr/bin/env perl6
use v6;
#
# In this code, a sudoku puzzle is represented as a two-dimentional
# array. The cells that are not yet solved are represented by yet
# another array of all the possible values.
#
# This implementation is not a simple brute force evaluation of all
# the options, but rather makes four extra attempts to guide the
# solution:
#
# 1) For every change in the grid, usually made by an attempt at a
# solution, we will reduce the search space of the possible values
# in all the other cells before going forward.
#
# 2) When a cell that is not yet resolved is the only one that can
# hold a specific value, resolve it immediately instead of
# performing the regular search.
#
# 3) Instead of trying from cell 1,1 and moving in sequence, this
# implementation will start trying on the cell that is the closest
# to being solved already.
#
# 4) Instead of trying all possible values in sequence, start with
# the value that is the most unique. I.e.: If the options for this
# cell are 1,4,6 and 6 is only a candidate for two of the
# competing cells, we start with that one.
#
# keep a list with all the cells, handy for traversal
my @cells = do for (flat 0..8 X 0..8) -> $x, $y { [ $x, $y ] };
#
# Try to solve this puzzle and return the resolved puzzle if it is at
# all solvable in this configuration.
sub solve($sudoku, Int $level) {
# cleanup the impossible values first,
if (cleanup-impossible-values($sudoku, $level)) {
# try to find implicit answers
while (find-implicit-answers($sudoku, $level)) {
# and every time you find some, re-do the cleanup and try again
cleanup-impossible-values($sudoku, $level);
}
# Now let's actually try to solve a new value. But instead of
# going in sequence, we select the cell that is the closest to
# being solved already. This will reduce the overall number of
# guesses.
for sort { solution-complexity-factor($sudoku, $_[0], $_[1]) },
grep { $sudoku[$_[0]][$_[1]] ~~ Array },
@cells -> $cell
{
my Int ($x, $y) = @($cell);
# Now let's try the possible values in the order of
# uniqueness.
for sort { matches-in-competing-cells($sudoku, $x, $y, $_) }, @($sudoku[$x][$y]) -> $val {
trace $level, "Trying $val on "~($x+1)~","~($y+1)~" "~$sudoku[$x][$y].perl;
my $solution = clone-sudoku($sudoku);
$solution[$x][$y] = $val;
my $solved = solve($solution, $level+1);
if $solved {
trace $level, "Solved... ($val on "~($x+1)~","~($y+1)~")";
return $solved;
}
}
# if we fell through, it means that we found no valid
# value for this cell
trace $level, "Backtrack, path unsolvable... (on "~($x+1)~" "~($y+1)~")";
return 0;
}
# all cells are already solved.
return $sudoku;
} else {
# if the cleanup failed, it means this is an invalid grid.
return False;
}
}
# This function reduces the search space from values that are already
# assigned to competing cells.
sub cleanup-impossible-values($sudoku, Int $level = 1) {
my Bool $resolved;
repeat {
$resolved = False;
for grep { $sudoku[$_[0]][$_[1]] ~~ Array },
@cells -> $cell {
my Int ($x, $y) = @($cell);
# which block is this cell in
my Int $bx = Int($x / 3);
my Int $by = Int($y / 3);
# A unfilled cell is not resolved, so it shouldn't match
my multi match-resolved-cell(Array $other, Int $this) {
return 0;
}
my multi match-resolved-cell(Int $other, Int $this) {
return $other == $this;
}
# Reduce the possible values to the ones that are still
# valid
my @r =
grep { !match-resolved-cell($sudoku[any(0..2)+3*$bx][any(0..2)+3*$by], $_) }, # same block
grep { !match-resolved-cell($sudoku[any(0..8)][$y], $_) }, # same line
grep { !match-resolved-cell($sudoku[$x][any(0..8)], $_) }, # same column
@($sudoku[$x][$y]);
if (@r.elems == 1) {
# if only one element is left, then make it resolved
$sudoku[$x][$y] = @r[0];
$resolved = True;
} elsif (@r.elems == 0) {
# This is an invalid grid
return 0;
} else {
$sudoku[$x][$y] = @r;
}
}
} while $resolved; # repeat if there was any change
return 1;
}
sub solution-complexity-factor($sudoku, Int $x, Int $y) {
my Int $bx = Int($x / 3); # this block
my Int $by = Int($y / 3);
my multi count-values(Array $val) {
return $val.elems;
}
my multi count-values(Int $val) {
return 1;
}
# the number of possible values should take precedence
my Int $f = 1000 * count-values($sudoku[$x][$y]);
for (flat 0..2 X 0..2) -> $lx, $ly {
$f += count-values($sudoku[$lx+$bx*3][$ly+$by*3])
}
for 0..^($by*3), (($by+1)*3)..8 -> $ly {
$f += count-values($sudoku[$x][$ly])
}
for 0..^($bx*3), (($bx+1)*3)..8 -> $lx {
$f += count-values($sudoku[$lx][$y])
}
return $f;
}
sub matches-in-competing-cells($sudoku, Int $x, Int $y, Int $val) {
my Int $bx = Int($x / 3); # this block
my Int $by = Int($y / 3);
# Function to decide which possible value to try first
my multi cell-matching(Int $cell) {
return $val == $cell ?? 1 !! 0;
}
my multi cell-matching(Array $cell) {
return $cell.grep({ $val == $_ }) ?? 1 !! 0;
}
my Int $c = 0;
for (flat 0..2 X 0..2) -> $lx, $ly {
$c += cell-matching($sudoku[$lx+$bx*3][$ly+$by*3])
}
for 0..^($by*3), (($by+1)*3)..8 -> $ly {
$c += cell-matching($sudoku[$x][$ly])
}
for 0..^($bx*3), (($bx+1)*3)..8 -> $lx {
$c += cell-matching($sudoku[$lx][$y])
}
return $c;
}
sub find-implicit-answers($sudoku, Int $level) {
my Bool $resolved = False;
for grep { $sudoku[$_[0]][$_[1]] ~~ Array },
@cells -> $cell {
my Int ($x, $y) = @($cell);
for @($sudoku[$x][$y]) -> $val {
# If this is the only cell with this val as a possibility,
# just make it resolved already
if (matches-in-competing-cells($sudoku, $x, $y, $val) == 1) {
$sudoku[$x][$y] = $val;
$resolved = True;
}
}
}
return $resolved;
}
my $puzzle =
map { [ map { $_ == 0 ?? [1..9] !! $_+0 }, @($_) ] },
[ 0,0,0,0,3,7,6,0,0 ],
[ 0,0,0,6,0,0,0,9,0 ],
[ 0,0,8,0,0,0,0,0,4 ],
[ 0,9,0,0,0,0,0,0,1 ],
[ 6,0,0,0,0,0,0,0,9 ],
[ 3,0,0,0,0,0,0,4,0 ],
[ 7,0,0,0,0,0,8,0,0 ],
[ 0,1,0,0,0,9,0,0,0 ],
[ 0,0,2,5,4,0,0,0,0 ];
my $solved = solve($puzzle, 0);
if $solved {
print-sudoku($solved,0);
} else {
say "unsolvable.";
}
# Utility functions, not really part of the solution
sub trace(Int $level, Str $message) {
say '.' x $level, $message;
}
sub clone-sudoku($sudoku) {
my $clone;
for (flat 0..8 X 0..8) -> $x, $y {
$clone[$x][$y] = $sudoku[$x][$y];
}
return $clone;
}
sub print-sudoku($sudoku, Int $level = 1) {
trace $level, '-' x 5*9;
for @($sudoku) -> $row {
trace $level, join " ", do for @($row) -> $cell {
$cell ~~ Array ?? "#{$cell.elems}#" !! " $cell "
}
}
}
Output:
Trying 8 on 9,1 [8, 9]
.Trying 6 on 9,2 [3, 6]
..Trying 7 on 9,9 [3, 7]
...Trying 1 on 9,8 [1, 3]
....Trying 4 on 8,1 [4, 5]
.....Trying 3 on 7,2 [3, 5]
......Trying 3 on 8,7 [2, 3]
.......Trying 6 on 8,9 [2, 6]
.......Trying 2 on 8,9 [2, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Trying 2 on 8,7 [2, 3]
.......Trying 3 on 8,9 [3, 6]
.......Trying 6 on 8,9 [3, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Backtrack, path unsolvable... (on 8 7)
.....Trying 5 on 7,2 [3, 5]
......Trying 5 on 8,7 [2, 5]
.......Trying 6 on 8,9 [2, 6]
.......Trying 2 on 8,9 [2, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Trying 2 on 8,7 [2, 5]
.......Trying 5 on 8,9 [5, 6]
.......Trying 6 on 8,9 [5, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Backtrack, path unsolvable... (on 8 7)
.....Backtrack, path unsolvable... (on 7 2)
....Trying 5 on 8,1 [4, 5]
.....Trying 3 on 8,3 [3, 4]
......Trying 6 on 8,9 [2, 6]
.......Trying 3 on 7,9 [3, 5]
........Trying 5 on 1,9 [2, 5]
.........Trying 3 on 3,8 [3, 7]
..........Trying 4 on 2,1 [1, 4]
..........Trying 1 on 2,1 [1, 4]
..........Backtrack, path unsolvable... (on 2 1)
.........Trying 7 on 3,8 [3, 7]
..........Trying 3 on 3,7 [1, 3]
..........Trying 1 on 3,7 [1, 3]
..........Backtrack, path unsolvable... (on 3 7)
.........Backtrack, path unsolvable... (on 3 8)
........Trying 2 on 1,9 [2, 5]
.........Trying 3 on 3,8 [3, 7]
..........Trying 7 on 2,7 [1, 7]
...........Trying 9 on 3,1 [2, 9]
...........Trying 2 on 3,1 [2, 9]
...........Backtrack, path unsolvable... (on 3 1)
..........Trying 1 on 2,7 [1, 7]
..........Backtrack, path unsolvable... (on 2 7)
.........Trying 7 on 3,8 [3, 7]
..........Trying 3 on 3,7 [1, 3]
..........Trying 1 on 3,7 [1, 3]
...........Trying 9 on 3,1 [2, 9]
...........Trying 2 on 3,1 [2, 9]
...........Backtrack, path unsolvable... (on 3 1)
..........Backtrack, path unsolvable... (on 3 7)
.........Backtrack, path unsolvable... (on 3 8)
........Backtrack, path unsolvable... (on 1 9)
.......Trying 5 on 7,9 [3, 5]
........Trying 8 on 1,9 [2, 8]
.........Trying 2 on 3,7 [1, 2]
.........Trying 1 on 3,7 [1, 2]
.........Backtrack, path unsolvable... (on 3 7)
........Trying 2 on 1,9 [2, 8]
.........Trying 7 on 3,8 [5, 7]
..........Trying 5 on 3,7 [1, 5]
...........Trying 2 on 2,1 [2, 4]
...........Trying 4 on 2,1 [2, 4]
...........Backtrack, path unsolvable... (on 2 1)
..........Trying 1 on 3,7 [1, 5]
...........Trying 9 on 3,1 [2, 9]
...........Trying 2 on 3,1 [2, 9]
...........Backtrack, path unsolvable... (on 3 1)
..........Backtrack, path unsolvable... (on 3 7)
.........Trying 5 on 3,8 [5, 7]
..........Trying 7 on 3,7 [1, 7]
...........Trying 2 on 2,1 [2, 4]
...........Trying 4 on 2,1 [2, 4]
...........Backtrack, path unsolvable... (on 2 1)
..........Trying 1 on 3,7 [1, 7]
..........Backtrack, path unsolvable... (on 3 7)
.........Backtrack, path unsolvable... (on 3 8)
........Backtrack, path unsolvable... (on 1 9)
.......Backtrack, path unsolvable... (on 7 9)
......Trying 2 on 8,9 [2, 6]
.......Trying 3 on 7,9 [3, 5]
........Trying 8 on 1,9 [5, 8]
.........Trying 3 on 3,8 [3, 7]
..........Trying 4 on 1,3 [1, 4]
...........Trying 9 on 1,1 [1, 9]
............Trying 1 on 3,1 [1, 2]
............Trying 2 on 3,1 [1, 2]
............Backtrack, path unsolvable... (on 3 1)
...........Trying 1 on 1,1 [1, 9]
...........Backtrack, path unsolvable... (on 1 1)
..........Trying 1 on 1,3 [1, 4]
...........Trying 9 on 1,1 [4, 9]
...........Trying 4 on 1,1 [4, 9]
...........Backtrack, path unsolvable... (on 1 1)
..........Backtrack, path unsolvable... (on 1 3)
.........Trying 7 on 3,8 [3, 7]
..........Trying 3 on 3,7 [1, 3]
..........Trying 1 on 3,7 [1, 3]
...........Trying 9 on 3,1 [2, 9]
...........Trying 2 on 3,1 [2, 9]
...........Backtrack, path unsolvable... (on 3 1)
..........Backtrack, path unsolvable... (on 3 7)
.........Backtrack, path unsolvable... (on 3 8)
........Trying 5 on 1,9 [5, 8]
........Backtrack, path unsolvable... (on 1 9)
.......Trying 5 on 7,9 [3, 5]
........Trying 5 on 1,8 [2, 5]
.........Trying 7 on 3,8 [2, 7]
..........Trying 4 on 1,3 [1, 4]
..........Trying 1 on 1,3 [1, 4]
..........Backtrack, path unsolvable... (on 1 3)
.........Trying 2 on 3,8 [2, 7]
..........Trying 9 on 3,1 [1, 9]
..........Trying 1 on 3,1 [1, 9]
..........Backtrack, path unsolvable... (on 3 1)
.........Backtrack, path unsolvable... (on 3 8)
........Trying 2 on 1,8 [2, 5]
.........Trying 7 on 3,8 [5, 7]
..........Trying 4 on 1,3 [1, 4]
...........Trying 9 on 1,1 [1, 9]
............Trying 1 on 3,1 [1, 2]
............Trying 2 on 3,1 [1, 2]
............Backtrack, path unsolvable... (on 3 1)
...........Trying 1 on 1,1 [1, 9]
...........Backtrack, path unsolvable... (on 1 1)
..........Trying 1 on 1,3 [1, 4]
...........Trying 9 on 1,1 [4, 9]
...........Trying 4 on 1,1 [4, 9]
...........Backtrack, path unsolvable... (on 1 1)
..........Backtrack, path unsolvable... (on 1 3)
.........Trying 5 on 3,8 [5, 7]
..........Trying 7 on 3,7 [1, 7]
...........Trying 2 on 2,1 [2, 4]
...........Trying 4 on 2,1 [2, 4]
...........Backtrack, path unsolvable... (on 2 1)
..........Trying 1 on 3,7 [1, 7]
..........Backtrack, path unsolvable... (on 3 7)
.........Backtrack, path unsolvable... (on 3 8)
........Backtrack, path unsolvable... (on 1 8)
.......Backtrack, path unsolvable... (on 7 9)
......Backtrack, path unsolvable... (on 8 9)
.....Trying 4 on 8,3 [3, 4]
......Trying 3 on 8,7 [2, 3]
.......Trying 6 on 8,9 [2, 6]
.......Trying 2 on 8,9 [2, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Trying 2 on 8,7 [2, 3]
.......Trying 3 on 8,9 [3, 6]
.......Trying 6 on 8,9 [3, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Backtrack, path unsolvable... (on 8 7)
.....Backtrack, path unsolvable... (on 8 3)
....Backtrack, path unsolvable... (on 8 1)
...Trying 3 on 9,8 [1, 3]
....Trying 4 on 8,1 [4, 5]
.....Trying 3 on 7,2 [3, 5]
.....Trying 5 on 7,2 [3, 5]
......Trying 6 on 7,9 [2, 6]
......Trying 2 on 7,9 [2, 6]
......Backtrack, path unsolvable... (on 7 9)
.....Backtrack, path unsolvable... (on 7 2)
....Trying 5 on 8,1 [4, 5]
.....Trying 6 on 8,9 [2, 6]
......Trying 8 on 1,9 [2, 8]
.......Trying 1 on 3,7 [1, 2]
.......Trying 2 on 3,7 [1, 2]
.......Backtrack, path unsolvable... (on 3 7)
......Trying 2 on 1,9 [2, 8]
.......Trying 7 on 3,8 [5, 7]
........Trying 5 on 3,7 [1, 5]
.........Trying 9 on 3,1 [1, 9]
.........Trying 1 on 3,1 [1, 9]
.........Backtrack, path unsolvable... (on 3 1)
........Trying 1 on 3,7 [1, 5]
.........Trying 9 on 3,1 [2, 9]
.........Trying 2 on 3,1 [2, 9]
.........Backtrack, path unsolvable... (on 3 1)
........Backtrack, path unsolvable... (on 3 7)
.......Trying 5 on 3,8 [5, 7]
........Trying 7 on 3,7 [1, 7]
.........Trying 9 on 3,1 [1, 9]
.........Trying 1 on 3,1 [1, 9]
.........Backtrack, path unsolvable... (on 3 1)
........Trying 1 on 3,7 [1, 7]
........Backtrack, path unsolvable... (on 3 7)
.......Backtrack, path unsolvable... (on 3 8)
......Backtrack, path unsolvable... (on 1 9)
.....Trying 2 on 8,9 [2, 6]
......Trying 5 on 1,8 [2, 5]
.......Trying 7 on 3,8 [2, 7]
........Trying 4 on 2,1 [1, 4]
........Trying 1 on 2,1 [1, 4]
........Backtrack, path unsolvable... (on 2 1)
.......Trying 2 on 3,8 [2, 7]
........Trying 9 on 3,1 [1, 9]
........Trying 1 on 3,1 [1, 9]
........Backtrack, path unsolvable... (on 3 1)
.......Backtrack, path unsolvable... (on 3 8)
......Trying 2 on 1,8 [2, 5]
.......Trying 7 on 3,8 [5, 7]
........Trying 1 on 3,7 [1, 5]
.........Trying 9 on 3,1 [2, 9]
.........Trying 2 on 3,1 [2, 9]
.........Backtrack, path unsolvable... (on 3 1)
........Trying 5 on 3,7 [1, 5]
.........Trying 9 on 3,1 [1, 9]
.........Trying 1 on 3,1 [1, 9]
.........Backtrack, path unsolvable... (on 3 1)
........Backtrack, path unsolvable... (on 3 7)
.......Trying 5 on 3,8 [5, 7]
........Trying 9 on 3,1 [1, 9]
........Trying 1 on 3,1 [1, 9]
........Backtrack, path unsolvable... (on 3 1)
.......Backtrack, path unsolvable... (on 3 8)
......Backtrack, path unsolvable... (on 1 8)
.....Backtrack, path unsolvable... (on 8 9)
....Backtrack, path unsolvable... (on 8 1)
...Backtrack, path unsolvable... (on 9 8)
..Trying 3 on 9,9 [3, 7]
...Trying 4 on 8,1 [4, 5]
....Trying 3 on 7,2 [3, 5]
....Trying 5 on 7,2 [3, 5]
.....Trying 6 on 7,9 [2, 6]
.....Trying 2 on 7,9 [2, 6]
.....Backtrack, path unsolvable... (on 7 9)
....Backtrack, path unsolvable... (on 7 2)
...Trying 5 on 8,1 [4, 5]
....Trying 6 on 8,9 [2, 6]
.....Trying 8 on 1,9 [2, 8]
......Trying 7 on 2,9 [2, 7]
.......Trying 1 on 3,7 [1, 2]
.......Trying 2 on 3,7 [1, 2]
.......Backtrack, path unsolvable... (on 3 7)
......Trying 2 on 2,9 [2, 7]
.......Trying 4 on 2,1 [1, 4]
.......Trying 1 on 2,1 [1, 4]
.......Backtrack, path unsolvable... (on 2 1)
......Backtrack, path unsolvable... (on 2 9)
.....Trying 2 on 1,9 [2, 8]
......Trying 3 on 3,8 [3, 5]
.......Trying 5 on 2,7 [1, 5]
........Trying 9 on 3,1 [2, 9]
........Trying 2 on 3,1 [2, 9]
........Backtrack, path unsolvable... (on 3 1)
.......Trying 1 on 2,7 [1, 5]
.......Backtrack, path unsolvable... (on 2 7)
......Trying 5 on 3,8 [3, 5]
.......Trying 3 on 3,7 [1, 3]
.......Trying 1 on 3,7 [1, 3]
.......Backtrack, path unsolvable... (on 3 7)
......Backtrack, path unsolvable... (on 3 8)
.....Backtrack, path unsolvable... (on 1 9)
....Trying 2 on 8,9 [2, 6]
.....Trying 5 on 1,8 [2, 5]
......Trying 3 on 3,8 [2, 3]
.......Trying 4 on 2,1 [1, 4]
.......Trying 1 on 2,1 [1, 4]
.......Backtrack, path unsolvable... (on 2 1)
......Trying 2 on 3,8 [2, 3]
.......Trying 9 on 3,1 [1, 9]
.......Trying 1 on 3,1 [1, 9]
.......Backtrack, path unsolvable... (on 3 1)
......Backtrack, path unsolvable... (on 3 8)
.....Trying 2 on 1,8 [2, 5]
......Trying 3 on 3,8 [3, 5]
.......Trying 4 on 1,3 [1, 4]
.......Trying 1 on 1,3 [1, 4]
.......Backtrack, path unsolvable... (on 1 3)
......Trying 5 on 3,8 [3, 5]
.......Trying 9 on 3,1 [1, 9]
.......Trying 1 on 3,1 [1, 9]
.......Backtrack, path unsolvable... (on 3 1)
......Backtrack, path unsolvable... (on 3 8)
.....Backtrack, path unsolvable... (on 1 8)
....Backtrack, path unsolvable... (on 8 9)
...Backtrack, path unsolvable... (on 8 1)
..Backtrack, path unsolvable... (on 9 9)
.Trying 3 on 9,2 [3, 6]
..Trying 7 on 9,9 [6, 7]
...Trying 1 on 9,8 [1, 6]
....Trying 4 on 8,1 [4, 5]
.....Trying 6 on 7,2 [5, 6]
......Trying 3 on 8,7 [2, 3]
.......Trying 6 on 8,9 [2, 6]
.......Trying 2 on 8,9 [2, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Trying 2 on 8,7 [2, 3]
.......Trying 6 on 8,9 [3, 6]
.......Trying 3 on 8,9 [3, 6]
.......Backtrack, path unsolvable... (on 8 9)
......Backtrack, path unsolvable... (on 8 7)
.....Trying 5 on 7,2 [5, 6]
......Trying 4 on 1,2 [2, 4]
.......Trying 1 on 1,3 [1, 5]
........Trying 2 on 2,1 [2, 5]
........Trying 5 on 2,1 [2, 5]
........Backtrack, path unsolvable... (on 2 1)
.......Trying 5 on 1,3 [1, 5]
........Trying 1 on 2,1 [1, 2]
.........Trying 9 on 1,1 [2, 9]
..........Trying 8 on 1,9 [2, 8]
..........Trying 2 on 1,9 [2, 8]
..........Backtrack, path unsolvable... (on 1 9)
.........Trying 2 on 1,1 [2, 9]
.........Backtrack, path unsolvable... (on 1 1)
........Trying 2 on 2,1 [1, 2]
.........Trying 9 on 1,1 [1, 9]
..........Trying 8 on 1,9 [2, 8]
...........Trying 2 on 8,9 [2, 3]
...........Trying 3 on 8,9 [2, 3]
...........Backtrack, path unsolvable... (on 8 9)
..........Trying 2 on 1,9 [2, 8]
..........Backtrack, path unsolvable... (on 1 9)
.........Trying 1 on 1,1 [1, 9]
..........Trying 8 on 1,9 [2, 8]
...........Trying 2 on 8,9 [2, 3]
...........Trying 3 on 8,9 [2, 3]
...........Backtrack, path unsolvable... (on 8 9)
..........Trying 2 on 1,9 [2, 8]
..........Backtrack, path unsolvable... (on 1 9)
.........Backtrack, path unsolvable... (on 1 1)
........Backtrack, path unsolvable... (on 2 1)
.......Backtrack, path unsolvable... (on 1 3)
......Trying 2 on 1,2 [2, 4]
.......Trying 1 on 2,1 [1, 5]
........Trying 9 on 1,1 [5, 9]
.........Trying 8 on 1,9 [5, 8]
.........Trying 5 on 1,9 [5, 8]
.........Backtrack, path unsolvable... (on 1 9)
........Trying 5 on 1,1 [5, 9]
........Backtrack, path unsolvable... (on 1 1)
.......Trying 5 on 2,1 [1, 5]
........Trying 9 on 1,1 [1, 9]
.........Trying 8 on 1,9 [5, 8]
..........Trying 6 on 7,9 [3, 6]
..........Trying 3 on 7,9 [3, 6]
..........Backtrack, path unsolvable... (on 7 9)
.........Trying 5 on 1,9 [5, 8]
.........Backtrack, path unsolvable... (on 1 9)
........Trying 1 on 1,1 [1, 9]
.........Trying 8 on 1,9 [5, 8]
..........Trying 5 on 8,9 [3, 5]
..........Trying 3 on 8,9 [3, 5]
..........Backtrack, path unsolvable... (on 8 9)
.........Trying 5 on 1,9 [5, 8]
.........Backtrack, path unsolvable... (on 1 9)
........Backtrack, path unsolvable... (on 1 1)
.......Backtrack, path unsolvable... (on 2 1)
......Backtrack, path unsolvable... (on 1 2)
.....Backtrack, path unsolvable... (on 7 2)
....Trying 5 on 8,1 [4, 5]
.....Trying 6 on 8,3 [4, 6]
......Trying 3 on 8,9 [2, 3]
.......Trying 6 on 7,9 [5, 6]
........Trying 5 on 1,9 [2, 5]
.........Trying 3 on 3,8 [3, 7]
..........Trying 4 on 2,1 [1, 4]
..........Trying 1 on 2,1 [1, 4]
..........Backtrack, path unsolvable... (on 2 1)
.........Trying 7 on 3,8 [3, 7]
..........Trying 3 on 3,7 [1, 3]
..........Trying 1 on 3,7 [1, 3]
..........Backtrack, path unsolvable... (on 3 7)
.........Backtrack, path unsolvable... (on 3 8)
........Trying 2 on 1,9 [2, 5]
.........Trying 3 on 3,8 [3, 7]
..........Trying 7 on 2,7 [1, 7]
..........Trying 1 on 2,7 [1, 7]
...........Trying 4 on 2,1 [2, 4]
...........Trying 2 on 2,1 [2, 4]
...........Solved... (2 on 2,1)
..........Solved... (1 on 2,7)
.........Solved... (3 on 3,8)
........Solved... (2 on 1,9)
.......Solved... (6 on 7,9)
......Solved... (3 on 8,9)
.....Solved... (6 on 8,3)
....Solved... (5 on 8,1)
...Solved... (1 on 9,8)
..Solved... (7 on 9,9)
.Solved... (3 on 9,2)
Solved... (8 on 9,1)
---------------------------------------------
9 5 4 1 3 7 6 8 2
2 7 3 6 8 4 1 9 5
1 6 8 2 9 5 7 3 4
4 9 5 7 2 8 3 6 1
6 8 1 4 5 3 2 7 9
3 2 7 9 6 1 5 4 8
7 4 9 3 1 2 8 5 6
5 1 6 8 7 9 4 2 3
8 3 2 5 4 6 9 1 7