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A few quick comments:

• Indeed, your solution doesn’t require \$N\$ to be odd. You’ve solved the slightly more general problem of finding a lonely integer in an array where every other element occurs at least twice, but could occur more often than that.

  Likewise, the restriction that \$N \leq 100\$ isn’t used, but I can’t think of how that could be used in a solution.

• I don’t know why you’ve defined a histogram() function, when you could swap it out for Counter(). That will make your code a little easier to read, because when I read Counter(), I immediately know what it does; if I see histogram() then I have to check I’ve understood the definition.

• When you iterate over the histogram, you should use .iteritems() instead of .items(); in Python 2.7 the latter is slower and more memory-expensive.

• You don’t need an explicit return None; Python will automatically return None if it drops out the end of a function.

• Rather than iterating over the tuples in Counter(array).items() and picking out the element/frequency by numeric index, it would be better to use tuple unpacking in the for loop:

   for elem, frequency in histogram(ary).items():
   if frequency == 1:
   return elem
  

  You could also just use the most_common() method on Counter(), and take the last element of that – but at that point you’re barely doing any work, so that might not be in the spirit of the problem.

A few quick comments:

• Indeed, your solution doesn’t require N to be odd. You’ve solved the slightly more general problem of finding a lonely integer in an array where every other element occurs at least twice, but could occur more often than that.

  Likewise, the restriction that N ≤ 100 isn’t used, but I can’t think of how that could be used in a solution.

• I don’t know why you’ve defined a histogram() function, when you could swap it out for Counter(). That will make your code a little easier to read, because when I read Counter(), I immediately know what it does; if I see histogram() then I have to check I’ve understood the definition.

• When you iterate over the histogram, you should use .iteritems() instead of .items(); in Python 2.7 the latter is slower and more memory-expensive.

• You don’t need an explicit return None; Python will automatically return None if it drops out the end of a function.

• Rather than iterating over the tuples in Counter(array).items() and picking out the element/frequency by numeric index, it would be better to use tuple unpacking in the for loop:

   for elem, frequency in histogram(ary).items():
   if frequency == 1:
   return elem
  

You could also just use the most_common() method of Counter, and take the last element of that – but at that point you’re barely doing any work, so that might not be in the spirit of the problem.