abcde.rb

ctr = 0

100000.times do |k|
  s = sprintf("%05d", k)
  a = s[0].to_i
  b = s[1].to_i
  c = s[2].to_i
  d = s[3].to_i
  e = s[4].to_i

  if a == 0  # only 5 digit numbers
    next
  end
  
  k1 = e
  if k1 == 0 or k % k1 != 0
    next
  end

  k2 = 10*d + k1
  if k2 == 0 or k % k2 != 0
    next
  end

  k3 = 100*c + k2
  if k3 == 0 or k % k3 != 0
    next
  end

  k4 = 1000*b + k3
  if k4 == 0 or k % k4 != 0
    next
  end

  ctr += 1

  s1 = sprintf("%01d", k1)
  s2 = sprintf("%02d", k2)
  s3 = sprintf("%03d", k3)
  s4 = sprintf("%04d", k4)

  puts "#{ctr}. #{a} #{b} #{c} #{d} #{e}"
  puts "  #{s} %    #{s1} = #{k % k1}    #{s} /    #{s1} = #{k / k1}"
  puts "  #{s} %   #{s2} = #{k % k2}    #{s} /   #{s2} = #{k / k2}"
  puts "  #{s} %  #{s3} = #{k % k3}    #{s} /  #{s3} = #{k / k3}"
  puts "  #{s} % #{s4} = #{k % k4}    #{s} / #{s4} = #{k / k4}"
end

http://math.stackexchange.com/questions/1182301/what-is-the-biggest-fivedigit-abcde-number-thats-divisible-by-bcde-cde