My coffee maker has settings for strong, gourmet, and bold. Which would brew the strongest coffee?
That depends on what you mean for strong.
Straing in flavor:
If you mean strong in flavor than you need to set the machine to a "fast" brew (Espresso in Italian).
The flavor gets extracted almost immediately from the grounds upon contact with water. You can visually judge how strong it is by the color: the darker the stronger. So the settings on your machine should be to use little water.
High in coffein:
If you mean high in coffein, than you need longer brew-time to extract this substance. As a rule of thumb the extraction is proportional to the time water stays in contact with coffee.
For coffee machines this means more water running through the grounds.
Note on "Fast Brew":
By "fast" I mean that it takes little time to make the coffee and not that the water runs faster through the grounds. The water runs always with same velocity, therefore if you use more water you'll wait more for your coffee. It takes less to make an espresso than to make an american coffee, obvioulsly.
Espresso vs American Coffee:
- Italian Espresso: strong in flavor
- Cup of american coffee: taste is deluted compared to Espresso but amount of coffein can be 8-10 times higher.