Digital Roots for 999

digital_root.rb

PEOPLE = [1, 2, 3, 4, 5, 6, 7, 8]

def subset(set)
  if set.empty?
    [[]]
  else
    first = set[0]
    rest = set[1..-1]
    
    subset(rest) + subset(rest).map { |x| x << first }
  end
end

def sum(set)
  set.inject(0) { |s, i| s + i }
end

def digital_root(set)
  s = sum(set)
  
  return s if s < 10
  new_set = s.to_s.split('').map { |x| x.to_i }
  digital_root new_set
end

all_groups = subset(PEOPLE).sort

valid_groups = all_groups.select { |p| p.length >= 3 && p.length <= 5 }

groups_without_junpei = valid_groups.reject { |g| g.include?(5) }
groups_with_snake = groups_without_junpei.select { |g| g.include?(2) }
groups_that_can_enter_3 = groups_with_snake.select { |g| digital_root(g) == 3 }

groups_that_can_enter_3.each { |g| puts g.inspect }

puts '*******************'

groups_without_snake = valid_groups.reject { |g| g.include?(2) }
groups_with_junpei = groups_without_snake.select { |g| g.include?(5) }
groups_with_june = groups_with_junpei.select { |g| g.include?(6) }
groups_that_can_enter_9 = groups_with_june.select { |g| digital_root(g) == 9 }


# groups_that_can_enter_9.each { |g| puts g.inspect }

puts '*******************'

base_groups = valid_groups.select { |g| digital_root(g) == 9 }

PEOPLE.each do |i|
  containing = base_groups.select { |g| g.include?(i) }.length
  puts "#{i}\t#{containing.to_f / base_groups.length}"
end