An answer for http://nabetani.sakura.ne.jp/hena/ord19nebasec/

Hd.pm

package Hd;
use strict;
use warnings;
use Exporter qw(import);
use List::MoreUtils qw(any);

our @EXPORT_OK = ('solve');


my $D = 192;
sub width ($) {
    my $r = shift;
    $D / ($r * 8);
}

sub range ($$) {
    my ($r, $n) = @_;
    my $w = width $r;
    my $off = $w / 2;
    if ($n == 0) {
        [0, $off - 1], [$D - $off, $D - 1];
    } else {
        my $x1 = $w * $n;
        my $x2 = $w * ($n + 1) - 1;
        [$x1 - $off, $x2 - $off];
    }
}

sub collision ($$) {
    my ($range1, $range2) = @_;
    $range2->[0] <= $range1->[0] && $range1->[0] <= $range2->[1] or
    $range2->[0] <= $range1->[1] && $range1->[1] <= $range2->[1] or
    $range1->[0] <= $range2->[0] && $range2->[0] <= $range1->[1] or
    $range1->[0] <= $range2->[1] && $range2->[1] <= $range1->[1];
}

sub parse   ($) { [/^(\d)(\d\d)$/] }
sub deparse ($) { sprintf '%01d%02d', @{$_[0]}}

sub collisions {
    my ($r, $ranges) = @_;

    my @result;
    for my $n (0 .. $r * 8 - 1) {
        my @ranges = range $r, $n;
        if (any {
            my $range = $_;
            any { collision $range, $_ } @$ranges;
        } @ranges) {
            push @result, deparse [$r, $n];
        }
    }

    return @result;
}

sub solve {
    my $input = shift;
    my @ngs = split /,/, $input;
    my %mark;
    for (@ngs) {
        my ($r, $n) = @{parse $_};
        my $n1 = ($n + 1) % ($r * 8);
        my $n2 = ($n - 1 + $r * 8) % ($r * 8);
        $mark{deparse [$r, $_]}++ for $n1, $n2;

        my @ranges = range $r, $n;

        if ($r > 1) {
            $mark{$_}++ for collisions $r - 1, \@ranges;
        }
        if ($r < 4) {
            $mark{$_}++ for collisions $r + 1, \@ranges;
        }
    }

    my @marks = grep { $mark{$_} >= 2 } sort keys %mark;
    @marks = grep { my $m = $_; ! any {$_ == $m} @ngs } @marks;
    @marks ? join ',', @marks : 'none';
}

1;

test.t

use strict;
use warnings;
use Test::More;
use Hd qw(solve);

while (<DATA>) {
    tr/\r\n//d;
    my ($n, $in, $out) = split /\t/, $_, 3;
    is solve($in), $out, "Q. $n";
}

done_testing;
__END__
0	400,401,302	300,301,402
1	105,100,306,414	none
2	100	none
3	211	none
4	317	none
5	414	none
6	100,106	107
7	205,203	102,204
8	303,305	304
9	407,409	306,408
10	104,103	207
11	204,203	102,305
12	313,314	209,418
13	419,418	314
14	100,102,101	201,203
15	103,206,309	205,207,308,310
16	414,310,309	206,311,413
17	104,102,206,307,102,202	101,103,203,204,205,207,308
18	104,206,308,409,407	103,205,207,306,307,309,408,410
19	313,406,213,301,409,422,412,102,428	none
20	101,300,210,308,423,321,403,408,415	none
21	304,316,307,207,427,402,107,431,412,418,424	none
22	205,408,210,215,425,302,311,400,428,412	none
23	200,311,306,412,403,318,427,105,420	none
24	105,305,407,408,309,208,427	104,209,306,406
25	311,304,322,404,429,305,316	203,303,321,405,406,430
26	210,401,316,425,101	211,315
27	414,403,404,416,428,421	303,415
28	207,300,103,211,428	104,206
29	322,314,310	none
30	427,200,215	100,323
31	311,402,424,307,318,430,323,305,201	200,204,301,302,306,322,423,425,431
32	425,430,408	none
33	202,320,209,426	319,427
34	430,209,302,310,304,431,320	202,303,323
35	208,206,406,424,213,312	207,311,313
36	420,302,313,413,317,402	301,403
37	319,306,309,418,204,411	305,307,308,412
38	400,308,105,430,203,428,209	104,210,429,431
39	200,305,214	215
40	214,408,410,407,317,422	306,316,409,423