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Perl 5, 295 bytes sub P{$r=$p/9;$c=$p%9;$q=3*~~($r/3)+$c/3}sub N{($i,$u)=@_;P;$G[$p]=$u*$i;$R[$r]{$i}=$C[$c]{$i}=$Q[$q]{$i}=$u}sub S{if($p>80){print@G;exit}if($G[$p]){S(++$p);$p--}else{N($_,1),S(++$p),$p--,N($_)for grep{P;$R[$r]{$_}+$C[$c]{$_}+$Q[$q]{$_}<1}1..9}}@G=split'',$ARGV[0];N($G[$p=$_],1)for 0..80;$p=0;S Try it online! Shortened from 339 to ...


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