Research patterns in "reverse substracting" numbers from themselves

reversed-subtraction.rb

#!/usr/bin/env ruby


# Bit of code to research patterns in "reverse substracting" numbers from themselves. Observations:
# * Mostly they reduce to zero; this can be by several routes:
#   * Quick
#   * 9's route (also: 99, 909, 999, 9009, 9999, 90009, 99099, 99999, etc.)
#   * 54-45 route (also: 54945, 549945, 5499945, 54999945, etc.)
# * End up in a loop, which is always by route of a 2 sets of "magic numbers":
#   * 2187, 21987, 219987, 2199987, 21999987, etc.
#   * 6534, 65934, 659934, 6599934, 65999934, etc.


# reduce a number by subtracting it from its reverse, and then take absolute of the result
def revsub(n)
  # we reverse in base10, hence the algorithm is base10 specific
  (n - n.to_s.reverse.to_i).abs
end

# true for numbers like 2178, 6534, 21978, 65934, 219978, 659934, 2199978, 6599934, etc.
# 2178: 2+7=9, 1+8=9;  6534: 6+3=9, 5+4=9; 2178 * 3 = 6534 (this also holds true outside of base10)
def is_magic1?(n)
  return false if n < 2178
  s = n.to_s
  ((s[0..1] == "21" && s[-2..-1] == "78") || (s[0..1] == "65" && s[-2..-1] == "34")) && s[2..-3] =~ /[9]*/
end


# TODO: define test for magic2, /[9]+[0]*[9]+/ || /54[9]*45/  # palindromes, but not all palindromes!


# keep some counts to get a grip on frequencies
c = {:looped => 0, :is_magic1 => 0, :by_5445 => 0, :nines => 0, :quick => 0}

(0..10000_000_000).each do |i|
  a = [i]
  r = i
  uniq = true
  while r > 0 && uniq
    # not many steps are needed, even when i grows really big
    r = revsub(r)
    uniq = !a.include?(r)
    a << r 
  end
  
  # do the counting
  c[:looped]    += 1   if !uniq
  c[:is_magic1] += 1   if is_magic1?(a[-1])
  c[:by_5445]   += 1   if a[-2] == 5445
  c[:nines]     += 1   if a[-2].to_s =~ /[9]+/
  c[:quick]     += 1   if a[-2] == i

  unless is_magic1?(a[-1])
    p [i, a.reverse[0..5]]
    p [:uniq, a] unless uniq
    p [:not_hidden, a] unless a[-2].to_s =~ /[9]+/ || a[-2] == i || a[-2] == 5445
  end
end