At the beginning of January, you set a goal to work every day, to reach a total of 5000 minutes of work by the end of the month. But to give yourself a better shot of achieving this, you decide to front-load it—at the beginning of each day, you figure out how much you’d need to work on average on each remaining day to achieve your goal, and then you work *double *the amount you need to do. For example, if you had 50 minutes left and 5 days left, you would need to work 10 minutes/day, so you would choose to work 20 minutes on that 5th-to-last day.

If you chose to work this way, how long does it take you to complete your goal of 5000 minutes?

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It takes you until the 2nd to last day (January 30th).

With this strategy, it will always be the 2nd to last day, regardless of how many days you have or how many minutes your goal is.

Think of it this way: if you have *x* minutes left and *y* days left, you would work *x* / *y* * 2. But this is always less than *x*, the number of minutes left, as long as *y* > 2. When *y* = 2, you would work exactly *x* minutes. Therefore, you’d always finish on the 2nd to last day.