I did some benchmarking about three years ago by timing myself trying to solve similarly-challenging Sudoku puzzles in a Nintendo DS game. With good sleep, I'd consistently approach 14 minutes with zero mistakes. After about 2-3 days of not having good sleep, it would drop to 16-20 minutes with more mistakes. I would also consciously notice various effects like diminished memory recall, more stuttering, poor focus, etc.
I've also been hearing that the length of sleep required is typically reduced with age. I don't have any citation on this though, would love to read more on the topic if anyone has more insight.
Of course there were many other variables like exercise, diet, health, and mood, where each seems to have some minor effect on my sleep requirements one way or the other. The Sudoku benchmarking was performed on more or less "idling" lifestyle (no unusual healthy or unhealthy activities, and I wasn't consuming alcohol/caffeine or smoking).
1: http://en.wikipedia.org/wiki/Free-running_sleep
2: http://www.supermemo.com/articles/sleep.htm#Free running sleep
As I've gotten older, it's become easy to fall asleep and wake up when I want to. Two things are critical to that:
1) no screen time in the 2 hours before bed. No TV, no computer. The only exception is reading books on my phone in night mode at the lowest setting.
2) no caffeine except for small amounts of chocolate.
My wife teases me because I can fall asleep in under a minute, and taking more than 10 minutes to fall asleep is actually one of the signs of a sleep disorder. (I don't have any of the other signs). It's not normal, but no TV or computer at night and no caffeine are not normal, either.
Having an office to go into and coworkers to be accountable to is the only thing that keeps me sane.
I always thought that it was a joke, but you can seriously try it and tell us how did it work.
If I've had several drinks (alcohol), I never sleep for 9 hrs, it's always less, but I haven't tracked post-alcohol sleep times closely enough to notice if it's still a multiple of 3.
However, I can also do 6 hrs or 3 hrs, and I don't feel groggy but I'll get tired sooner the next night. Not adhering to a multiple of 3 hrs (rem cycles I assume), or reasonably close to that, ends up badly.
What I really need is an alarm hooked up to a primitive EEG so that it can start the clock when I fall asleep, and set off an alarm after a programmable number of minutes. That way I could sleep for 6 hrs without ever being groggy. But even the cheapest EEG stuff I've seen connectable to a computer is not cheap.
There are various devices for sleep enhancement, e.g. "the sleep watch"[1]. I haven't tested any of them, though (nobody ships stuff to Russia).
It's nice not waking up groggy because my alarm is timed to my EEGs.
Being able open your eyes, refreshed, some time early in the morning, without the need for any alarm, is as good as it gets. This is well within reach if you don't have any dependants.
I need to get back to that. I feel so much worse without it.
When I undersleep, I struggle to oversleep. It is hard, but needed anyway.