Yeah, there are diminishing returns to adding more shortcuts.

Technically, $grid_v is not needed at all.

return if index(substr($grid_v, $x*$size, $size), $n) >= 0;
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can be written as

foreach my $y_ (0 .. $size-1) {
   return if substr($grid_h, $y_*$size+$x, 1) eq $n;
}
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I just thought the former would be faster, even though we must constantly make copies of $grid_v in addition to $grid_h.