Visualize a Nim board like an expert
Python 2, 150 196 206 bytes



def f(p):
 c=48;s=[l*'.'for l in p];m=2**len(bin(l))
 while m:
  if sum(m*'.'in l for l in s)&gt;1:
   for i,l in enumerate(s):s[i]=l.replace('.'*m,chr(c)*m,`s`.count(chr(c)*m)&lt;2)
   c+=1
  else:m/=2
 return s


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