Alternative approaches to comparing values

This problem can be greatly simplified, without loss of generality, by sorting:

def close_far(a, b, c):
  x, y, z = sorted([a, b, c])
  delta_close, delta_far = sorted([y - x, z - y])
  return delta_close <= 1 and delta_far >= 2

def close_far(a, b, c):
    def close(x, y): return abs(x - y) <= 1
    def far(x, y): return abs(x - y) >= 2
    return (close(b, a) and far(c, a) and far(c, b) or
            close(c, a) and far(b, a) and far(b, c))

>>> close_far(1, 2, 10)
True
>>> close_far(1, 2, 3)
False
>>> close_far(4, 1, 3)
True

Little help:

def close_far(a, b, c): return ((abs(a-c) >= 2 and abs(a-b) <= 1) and (abs(b-c) >= 2)) or ((abs(a-c) <= 1 and abs(a-b) >= 2) and (abs(b-c) >= 2))

Here is an approach:

def close_far(a, b, c):
    return not ((is_close(a,b)==is_close(a,c)) or is_close(b,c))


def is_close(num1, num2):
    return abs(num1-num2)<=1