**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