Weightloss on autopilot (a.k.a. controlled yo-yo diet, a.k.a the Binge'n'Fast diet)
Warning: This is for scientifically minded people.
It may seem too hardcore for some timid souls.
I'm not responsible if you get ill or die because of using this method irresponsibly 
Anyway: here is how you lose x kg (or x lbs) in y days.
Prerequisites:
1. A good scale (a digital one with 0.1 kg steps is adequate)
2. A modicum of willpower
The algoritm:
1. Weigh yourself to determine your initial weight.
2. Decide your goal weight.
3. Decide (realistically) by which date you wish to have reached your goal weight. Calculate the total number of days between now and then.
4. On each morning between now and the goal date, do the following:
4.I Weigh yourself.
4.II Calculate the goal weight for this day. The formula is:
start weight + (goal weight - start weight) * (day number / total number of days)
4.III a) If your actual weight is less than or equal to your goal weight for this day then:
Consume
as much as you want of
anything you want for the next 24 hours.
4.III b) If your actual weight is greater than your goal weight for this day then:
Do not consume
anything except water for the next 24 hours. You may drink as much water as you like though.
By repeating steps 4.I to 4.III you will reach your goal weight by the predetermined date (+/- a couple of days)
This works in a similar way to the autopilot of an aircraft.
The plane may be naturally drifting quite a bit to one side or another,
but the drift is constantly measured and compensated for,
and the long-term average course is a straight line from A to B.
I'm not necessarily saying that this "diet" is healthy
, but it works if your only goal is weightloss.
No calorie counting, no special foods, only a series of controlled mini-fasts.
There are several ways to make the ride more enjoyable:
1. Choose a slower weightloss rate. 0.1 kg per day was quite comfortable for me.
2. Relax the water-only requirement in step III b.
E.g. drink only juices.
3. Measure your weight 2 or more times a day, for shorter (less painful) periods of food deprivation.
4. Don't binge just because you can. You know you'll have to pay for it tomorrow.