Would this number make a good 2048 combo?
Python: 457 422 characters
z=range
def c(n):
 for x in z(1,12): 
  if int(n)==2**x:return 1
 return 0
def p(s):
 if s=='':return[]
 for i in z(len(s),0,-1):
  if c(s[:i])&gt;0and p(s[i:])!=1:return [int(s[:i])]+p(s[i:])
 return 1
def r(a):
 if len(a)==1:return 1
 i,t=1,a[:1]
 while i&lt;len(a):
  if a[i]==t[-1]:t[-1]*=2
  else:t+=[a[i]]
  i+=1
 if len(t)==len(a):return 0
 return r(t) 
def f(s):
 if p(s)==1or r(p(s))==0:print('bad')
 else:print('good')

The function f(s) gets a string of digits and outputs 'good' or 'bad' accordingly.
I chose not to use 0 as spaces because spaces are meaningless in the game and they create ambiguity when parsing strings (is 22048 good or bad?). This only uses numbers up to 2048, but that can be changed without adding characters.
At the cost of 10 characters or so I can also print all the steps of combining the numbers.
And I realize that this code isn't golfed enough yet; don't worry, edits are coming.