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

yhpg.rb

def angle_of(sector)
  div, mod = sector.divmod(100)
  angle = { 1 => 360 / 8r, 2 => 360 / 16r, 3 => 360 / 24r, 4 => 360 / 32r }[div]
  base = angle / 2
  if mod.zero?
    [base, base + (div * 8 - 1) * angle]
  else
    [base + angle * mod, base + angle * (mod - 1)]
  end
end

def neighboring_sector?(sector, target)
  b = target[0] < sector[0] && sector[1] < target[0]
  b ||= target[1] < sector[0] && sector[1] < target[1]
  b ||= sector[0] < target[0] && target[1] < sector[0] && sector[1] < target[0] && target[1] < sector[1]
  b ||= sector[0] < sector[1] && target[0] < target[1]
  b ||= sector[0] < sector[1] && sector[0] < target[0] && target[1] < sector[0]
  b ||= sector[0] < sector[1] && sector[1] < target[0] && target[1] < sector[1]
  b
end

def neighboring_sector_of(sector)
  div, mod = sector.divmod(100)
  targets = {
    1 => (200..215).to_a,
    2 => (100..107).to_a + (300..323).to_a,
    3 => (200..215).to_a + (400..431).to_a,
    4 => (300..323).to_a
  }[div]

  sector_angle = angle_of(sector)

  # 内側・外側のセクタの計算
  # 初期値は両端のエッジ
  edges = [
    div * 100 + (mod.zero? ? div * 8 - 1 : mod - 1),
    div * 100 + (mod == div * 8 - 1 ? 0 : mod + 1)
  ]
  ans = targets.each_with_object(edges) do |target, ary|
    target_angle = angle_of(target)
    ary << target if neighboring_sector?(sector_angle, target_angle)
  end

end

def solve(src)
  sectors = src.split(",").map(&:to_i)
  return "none" if sectors.size == 1
  targets = sectors.each_with_object([]) do |sector, ary|
    ary << neighboring_sector_of(sector)
  end

  ans = targets.
    flatten.
    group_by { |e| e }.
    select { |k, v| 2 <= v.size }.
    keys.
    select { |e| !sectors.include?(e) }.
    sort.
    join(",")
  ans.empty? ? "none" : ans
end

DATA.readlines.each do |line|
  no, src, expected = line.split(/\s/)
  actual = solve(src)
  result = actual == expected ? "ok" : "***NG***"
  puts "#{no}: " + result
end

__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