project_euler_112.rb

# Bouncy numbers
# Problem 112
# Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.
#
# Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.
#
# We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.
#
# Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.
#
# Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.
#
# Find the least number for which the proportion of bouncy numbers is exactly 99%.

least = 100
bouncy_count = 0

def bouncy?(i)
  !(increasing?(i) || decreasing?(i))
end

def increasing?(i)
  i.to_s.chars.sort.join == i.to_s
end

def decreasing?(i)
  i.to_s.chars.sort.reverse.join == i.to_s
end

loop.with_index(least) do |_, i|
  bouncy_count += 1 if bouncy?(i)
  if bouncy_count * 100 / i == 99
    puts i
    break
  end
end