On that 4096 question I almost allowed hubris to lead me into the trap of thinking about powers of 2 exclusively. I was very proud of myself that I could quickly do powers of 2 up to 4096 in my head and immediately recognized the question as a prime favtoring question and was ready to congratulate myself on a job well done when I, just for the sake of completeness, considered if there was any other way we could get x and y to be further apart. Alas 4096^1! I am assuming the answer is 4095. That is some nasty stuff!
Actually now that I am looking back at it x had to be the base and y the exponent so even if the base were 2 the answer would have been negative and would have been less negative of the base were 4 or something larger than 2 so even for that reason x should not have been 2. Just goes to show you what happens when you do before you think instead of the other way around!