# Euler Solution 112

### From ProgSoc Wiki

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%.

## Python by Althalus

With this problem, progsoc has now reached level 3. Runtime: 24sec

def bounce(n): n = [int(x) for x in str(n)] up,down,check = False,False, n[0] for c in n: if c > check: up = True if c < check: down = True if up and down: return True check = c return False def infGen(start=0,iter=1): #Why? Because I can :) count = start while 1: count +=iter yield count count,test = 525,1000 inf = infGen(1000) for x in inf: if x % 100000 == 0: print x if bounce(x): count+=1 test +=1 if count*100.0/test == 99.0: print '99%: ', x; break