Contest

I feel obligated to preface what follows with the comment that I think contests like that are a bad plan: They reward people who are more willing to take health risks, and ignore issues of sustainability and learning to maintain.

If you want to maximize calorie burn through exercise over a fairly short time period (short number of weeks, tops), the sweet spot for calorie burn is usually to identify the amount of time you're willing to devote daily to exercise, and spend it on cardio, structured as:

1. A short warm-up,
2. Steady state intensity for the overwhelming fraction of the time (at the highest intensity you can sustain for that time period without becoming too exhausted to finish, without having fatigue afterward that reduces your daily-life calorie expenditure, and without putting you in a position where you can't fully recover before the next workout), and
3. Wrapping up up with a short cool-down.

This would give you the maximum calorie burn, and it's calorie balance that determines weight loss.

What would be much more sensible for your health and well-being would be to divide your time between cardio you enjoy, and some strength training, because it's a better plan to preserve muscle while losing fat, and strength training helps with that. Optimally for both fitness and sustainable weight loss, it's good to phase in an exercise program gradually and manageably, not go from minimal to maximum all in one jump.

That exercise schedule would ideally be combined with a fully nutritious, calorie appropriate way of eating (not losing too fast, for sure less than 1% of current body weight weekly - possibly much less, depending on current weight and other factors (with the exception that someone morbidly obese may be able to lose faster than 1% for a while, if under close medical supervision).

TV shows like "Biggest Loser" have given people really toxic ideas about how to lose weight, and essentially no idea at all about how to lose weight in a way that helps one sustain that loss long term.

Best wishes as you strive to accomplish your goals, sincerely.

Agreeing with Ann and Pav. While a contest (more specifically the cash prize) may seem like a good incentive, you pretty much can't win unless you're willing to go to extremes and risk your health, because at least one other person will be doing that.