http://nabetani.sakura.ne.jp/hena/ordf01_twicel/ への回答

main.rb

Point = Struct.new(:color, :x, :y)

def hoge(arg)
  rows = arg.split("/").map { |s| sprintf("%08b", s.to_i(16)).chars }

  yoko = rows.flat_map.with_index { |row, _y|
    row.map.with_index.chunk(&:first).map { |color, ary|
      ary.map { |_, _x| Point.new(color, _x, _y) }
    }.select { |a| a.size > 1 }
  }

  tate = rows.transpose.flat_map.with_index { |row, _x|
    row.map.with_index.chunk(&:first).map { |color, ary|
      ary.map { |_, _y| Point.new(color, _x, _y) }
    }.select { |a| a.size > 1 }
  }

  [
    *yoko.select { |yoko_group| tate.all? { |tate_group| (yoko_group & tate_group).empty? } },
    *tate.select { |tate_group| yoko.all? { |yoko_group| (tate_group & yoko_group).empty? } }
  ].
    select { |a| a.size == 2 }.
    group_by { |a| a.map(&:color).uniq.first }.
    tap { |h| break h.values_at("0", "1").map(&:to_a).map(&:size).join(",") }
end

require 'test-unit'

class HogeTest < Test::Unit::TestCase
  TEST_CASES = DATA.each_line.map { |line|
    %r[^/\*(?<id>\d+)\*/.*test\((?<act_exp>.*)\)] =~ line
    act, exp = act_exp.scan(%r["(.+?)"]).flatten
    [id, [act, exp]]
  }.to_h

  data(TEST_CASES)
  test "hoge" do |(actual, expected)|
    assert_equal(hoge(actual), expected)
  end
end

__END__
/*0*/ test( "dc/bc/a7/59/03/d5/d4/ea", "2,3" );    
/*1*/ test( "ff/ff/ff/ff/ff/ff/ff/ff", "0,0" );    
/*2*/ test( "00/00/00/00/00/00/00/00", "0,0" );    
/*3*/ test( "cc/33/cc/33/cc/33/cc/33", "16,16" );    
/*4*/ test( "aa/aa/55/55/aa/aa/55/55", "16,16" );    
/*5*/ test( "ac/a3/5c/53/ca/3a/c5/35", "8,8" );    
/*6*/ test( "db/00/db/00/db/00/aa/aa", "0,13" );    
/*7*/ test( "24/24/db/24/24/db/24/24", "0,12" );    
/*8*/ test( "d7/d7/e9/f1/f7/de/60/56", "3,2" );    
/*9*/ test( "17/7d/64/9b/a5/39/53/a6", "2,2" );    
/*10*/ test( "bb/8f/18/fb/89/c2/c7/35", "1,2" );    
/*11*/ test( "6d/63/20/08/54/cd/32/4f", "2,2" );    
/*12*/ test( "a9/ca/cd/46/99/e6/f0/30", "2,2" );    
/*13*/ test( "5b/70/fd/45/e2/a1/ab/9a", "1,2" );    
/*14*/ test( "24/e4/a8/12/e1/a6/3f/f3", "2,1" );    
/*15*/ test( "79/32/2e/07/d5/10/e7/9d", "2,2" );    
/*16*/ test( "60/bc/ab/ec/1f/eb/63/2c", "4,2" );    
/*17*/ test( "a5/dd/92/4e/67/c6/dc/34", "6,1" );    
/*18*/ test( "aa/96/6d/67/d2/a8/ac/90", "3,2" );    
/*19*/ test( "95/72/7d/5c/47/dc/ef/99", "4,0" );    
/*20*/ test( "17/d6/6a/27/1f/25/26/b8", "2,1" );    
/*21*/ test( "f0/f3/76/c5/31/ca/6b/ae", "1,2" );    
/*22*/ test( "01/59/26/fa/8c/70/12/cd", "1,4" );    
/*23*/ test( "1a/c3/1f/0b/83/b6/81/0d", "0,5" );    
/*24*/ test( "4c/49/05/cf/54/bb/1f/da", "1,2" );    
/*25*/ test( "eb/7c/d5/09/2a/c2/14/6b", "0,7" );    
/*26*/ test( "b4/d3/4c/c4/ed/19/e8/63", "1,3" );    
/*27*/ test( "bd/bc/6d/60/9b/00/9a/32", "2,4" );    
/*28*/ test( "94/97/3f/e3/c7/06/15/c0", "2,2" );    
/*29*/ test( "5f/1d/67/16/b8/f7/0a/2a", "2,2" );    
/*30*/ test( "df/e6/f9/4f/59/e9/1f/ee", "3,0" );    
/*31*/ test( "5a/53/9a/9a/73/b4/37/07", "3,2" );    
/*32*/ test( "bd/87/7c/e7/c0/37/82/da", "2,3" );    
/*33*/ test( "3d/c0/13/ac/57/3d/15/78", "2,2" );    
/*34*/ test( "63/64/54/3a/40/28/4e/4e", "0,3" );    
/*35*/ test( "f6/81/c9/15/00/4c/a0/a8", "1,4" );    
/*36*/ test( "19/41/df/f8/e3/74/6b/9b", "4,2" );    
/*37*/ test( "d5/0b/dd/35/3b/d2/0b/6b", "1,5" );    
/*38*/ test( "08/b7/91/f3/6e/3c/74/a0", "0,0" );    
/*39*/ test( "b8/a8/b4/a6/93/2c/94/3f", "0,0" );    
/*40*/ test( "88/22/21/ee/dc/19/43/01", "0,0" );    
/*41*/ test( "e1/ee/35/bc/fc/00/8e/fe", "0,0" );    
/*42*/ test( "3c/42/63/5f/27/47/07/90", "0,0" );