Problem 112

Problem: 

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%.


My Solution:

def isInc(n):
  dummy = True
  n=str(n)
  for i in range(1,len(n)):
    if int(n[i]) < int(n[i-1]):
      dummy = False
  return dummy

def isDec(n):
  dummy = True
  n=str(n)
  for i in range(1,len(n)):
    if int(n[i]) > int(n[i-1]):
      dummy = False
  return dummy
  
def isBouncy(n):
  dummy=False
  if not isInc(n) and not isDec(n):
    dummy=True
  return dummy

bouncy=[]
i=21780

while (len(bouncy)+.9*21780)/i < .99:
  i=i+1 
  if isBouncy(i):
    bouncy.append(i)

print i