12s.rb

#!/usr/bin/env ruby
#
# Solutions to Diamond Geezer's "the digits of the year 2019 add up to twelve" puzzles:
# http://diamondgeezer.blogspot.com/2019/01/the-digits-of-year-2019-add-up-to-twelve.html

def main
  # a) How many years ago did this last happen?
  a = 2019 - 2018.downto(0).find { |year| sum_digits(year) == 12 }
  # b) In what year?
  b = 2018.downto(0).find { |year| sum_digits(year) == 12 }
  # c) How many years until it next happens?
  c = 2020.upto(9999).find { |year| sum_digits(year) == 12 } - 2019
  # d) In what year?
  d = 2020.upto(9999).find { |year| sum_digits(year) == 12 }

  # e) How many times will it happen this century?
  e = 2001.upto(2100).map { |year| [year, sum_digits(year)] }.count { |year, sum| sum == 12 }
  # f) What's the maximum number of times it can happen in a century?
  f = 1.upto(9999).each_slice(100).map { |c| [c.first, c.map { |year| [year, sum_digits(year)] }.count { |year, sum| sum == 12 }] }.max { |a, b| a[1] <=> b[1] }.last
  # g) In which century will this maximum next happen?
  g = 2001.upto(9999).each_slice(100).map { |c| [c.first, c.map { |year| [year, sum_digits(year)] }.count { |year, sum| sum == 12 }] }.find { |year, sum| sum == f }.first
  g = century(g)
  # h) In which century did this maximum last happen?
  h = 1.upto(2000).each_slice(100).map { |c| [c.first, c.map { |year| [year, sum_digits(year)] }.count { |year, sum| sum == 12 }] }.find_all { |year, sum| sum == f }.last.first
  h = century(h)

  # i) When will there next be a 99-year gap?
  i = 2019.upto(99999).map { |year| [year, sum_digits(year)] }.select { |year, sum| sum == 12 }.each_cons(2).find { |a, b| b[0] - a[0] == 99 }.map { |a| a.first }
  i = "Between the years #{i[0]} and #{i[1]}"
  # j) When will there next be a longer gap?
  j = 2019.upto(99999).map { |year| [year, sum_digits(year)] }.select { |year, sum| sum == 12 }.each_cons(2).find { |a, b| b[0] - a[0] > 99 }.map { |a| a.first }
  j = "Between the years #{j[0]} and #{j[1]}"
  # k) When is the next century with no years when this happens?
  k = 2001.upto(9999).each_slice(100).map { |c| [c.first, c.map { |year| [year, sum_digits(year)] }.count { |year, sum| sum == 12 }] }.find { |year, sum| sum == 0 }.first
  k = century(k)
  # l) How many times will it happen this millennium?
  l = 2001.upto(3000).map { |year| [year, sum_digits(year)] }.count { |year, sum| sum == 12 }

  ("a".."l").each do |v|
    puts "#{v}) #{binding.local_variable_get(v.to_sym)}"
  end
end

def sum_digits(year)
  year.to_s.chars.map(&:to_i).reduce(:+)
end

def ordinal(num)
  case num.to_s
  when "11", "12", "13"
    "#{num}th"
  when /1$/
    "#{num}st"
  when /2$/
    "#{num}nd"
  when /3$/
    "#{num}rd"
  else
    "#{num}th"
  end
end

def century(year)
  ordinal((year / 100).floor + 1)
end

main