Back when I was working in a commercial gym, I got asked by a potential client (who then didn't hire me after hearing my answer) how to lose 10kg in 3 weeks for a wedding. She insisted that this was a realistic goal. I gave a rough breakdown of what it would take to lose 10kg of fat in that time. I don't know if she got disheartened and gave up on her plan, or if she decided to take her business elsewhere, all I know is that I didn't hear from here again.
Now, let's pretend that you're her and you want to lose 10kg in 3 weeks. In reality, you can get somewhat of a boost on that amount through water loss, but I've never been in the business of getting pseudo-results for clients. So let's go with an actual 10kg of fat.
According to one of my textbooks, 1g of fat contains roughly 9.4kcal. That puts 1kg of fat at 9,400kcal, and 10kg of fat at 94,000kcal.
According to the back of my cereal boxes, the average adult's daily intake is something like 2,400kcal. Let's assume that that's accurate, and that the adult in question is maintaining weight at that level.
You've got 21 days to work with, so 94,000 / 21 ~ 4,475kcal. That's the daily calorie deficit we're after. Let's assume (unwisely) that the person's metabolic rate doesn't shift at all in the process. To simplify things, here are a couple ways that our client could hypothetically achieve that calorie deficit:
1) Burn 4,475kcal/day through additional physical activity while maintaining current diet.
2) Consume 0kcal/day, and burn 2,075kcal/day through additional physical activity (4,475 - 2,400 = 2,075).
3) Consume a diet of -2,075kcal/day by eating things that can only be identified through theoretical physics.
Let's assess the viablity of these three options.
The third option, involving no additional exercise (yay for laziness) but eating a solid diet of anti-matter is about as close to impossible as can be. We can rule that out right off the bat.
As for the other two options, lets look at where exercise will lead us.
According to Lyle McDonald, the average person can, at a maintainable pace, burn roughly 5-10kcal/min, which clocks up 300-600kcal/hr (average 450kcal/hr). 4,475 / 450 ~ 9.9. So, we'd be looking at roughly 10 hours of exercise per day in the first option to lose 10kg of fat over 3 weeks. 2,075 / 450 ~ 4.6. So in the second option, we're looking at a little over 4hr30min of exercise in order to lose that weight. That probably sounds less awful than 10 hours, but remember you're doing this on a thoroughly empty stomach -- three weeks without a single calorie entering your body.
So, is it theoretically possible to lose that amount of fat in 3 weeks. Yes. Is it realistic? Only if you can make exercise a full-time job for the duration of that 3wk window whilst avoiding problems with metabolism and health.
Now let's bring this same math over to more realistic goals. Let's say you want to lose weight, and you're going to do it through exercise, without changing your eating habits to suit fat loss. Remember, 1 hour of maintainable exercise will burn an average of 450kcal, and 1kg of fat contains roughly 9,400kcal. 9,400 / 450 ~ 20.9. That means it'll take almost 21 hours of exercise to lose 1kg of fat. If you're doing the 30min/day, 5 days/wk recommended by the government, you'll have lost your first kilo after about 8-9 weeks. If you double the duration of each session to 1hr, you can halve the time required to lose 1kg down to 4 weeks. And if you do 1hr/day, every single day, you can lose 1kg through exercise alone in 3 weeks.
Yes, an hour a day, daily, will (theoretically) give you a 1kg loss in fat after 3 weeks of exercise. 3 weeks, the time in which 10kg, evidently, is not so realistic.
What shall we take away from this?
Firstly, get realistic. Weight loss is a slow process, or at least it's slower than the marketing machine would have you believe. Fortunately it doesn't take many kilos of fat loss to make a difference to most people's bodies, but still, if you're focused on the scale and you're doing things properly, you may be in for a rude wake-up call.
Secondly, the importance of nutrition. Most people don't have the desire or priorities in place to do an hour of exercise a day, every day. Most people, despite their protests to the contrary, do have the time for it, but are focused on other things, and probably see exercise as a chore, and so an hour a day is unlikely to occur. It takes an hour to burn 450kcal in the gym. It takes no time at all to not put 450kcal worth of doughnuts (which is 2xKrispy Kremes) or soft drink into your body. If you're consuming 5 meals a day, you can easily reduce your calorie consumption by 450kcal/day by reducing each meal by 75kcal. Not such a tough deal.