Coffee Problem

published 2026-03-06

by Christopher Howard

Actually, I don't drink coffee. I tried black coffee a few months ago, but I just didn't like it. I had decided that, if I didn't like coffee black, I wasn't going to drink it at all. None of this wimpy creamer nonsense.

Nonetheless, I was presented with a related arithmetic problem a few weeks back. There was a big crew of pilots coming in for a training class, and I needed to make a pot of coffee in the pilots lounge. Sounds straightforward enough. But there were a few little quirks in this particular case. The coffee on hand was a container of Maxwell coffee, which looks like it had been there since 1987.

I wanted to make one pot of coffee, which according to the markings on the pot, was 12 cups of coffee.
The Maxwell container specified that I needed ½ cups of grinds to make 10 servings of coffee.
According to said container, one serving is 6 ounces of coffee, as opposed to the usual 8 ounces per cup.
There was not any measuring device nearby for measuring out cups of grinds. I.e., no measuring cups that specified a cup or ½ a cup. There were some coffee mugs nearby, of course, but I didn't know how many standard cups fit inside any of the mugs.
There were some plastic spoons nearby, which appeared to be roughly the size of a tablespoon, maybe slightly smaller. I had seen a real measuring tablespoon recently, so I felt confident the plastic spoon would be close enough, if I had the spoon slightly overfilled with grinds.

So, how many tablespoons of grinds would I need to make the pot of coffee? Of course, being a slide rule enthusiast, no digital calculators are allowed.

I'm obsessed with ratios, so I tried to lay this out as a ratio problem. We have these data points from the coffee making materials:

12 cups coffee ∶ 1 pot coffee
½ cups grinds ∶ 10 servings coffee
6 oz coffee ∶ 1 servings coffee

We will need this other common-knowledge data:

8 oz coffee ∶ 1 cup coffee
16 tablespoons grinds ∶ 1 cup grinds

Let's reorganize this, and put all the unity values on the right side:

12 cups coffee ∶ 1 pot coffee
8 oz coffee ∶ 1 cup coffee
⅙ servings coffee ∶ 1 oz coffee
1/20 cups grinds ∶ 1 servings coffee
16 tablespoons grinds ∶ 1 cup grinds

Laid out this way, it becomes a multiplication problem, where we just multiply together all the ratios or fractions. But what is the simplest way to do this on a slide rule, without having to write down a bunch of intermediate values? The simple approach is as so: line up the index on the middle C scale with the 1.2 on the bottom D scale, setting the initial ratio. Slide the cursor over to 8 on the C scale. Then align the index on the C scale with the cursor.

Then, move the cursor over to ⅙ on the C scale. Rather than calculating ⅙ separately, we use 6 on the CI scale. Then move the index on the C scale over to the cursor. And so on for 1/20 and 16.

When I did this, the result I got was 1.28. Now for the scaling: If we do a bunch of rounding, we can solve this simple multiplication problem in our head:

10 × 10 × 1/5 × 1/20 x 15

Ten times ten is one-hundred... divided by five is twenty... divided by twenty is one... multiplied by 15 is 15. So, our answer should be somewhere in the ball-park of 15 tablespoons. If we scale up 1.28 by ten, we get 12.8 tablespoons, which we will round up to 13 tablespoons.

I used 13 tablespoons, setting the coffee maker to "strong" brew. The coffee came out looking okay, and nobody complained about it. Mission accomplished!

I asked a pilot how much grinds they use. Normally they just dump a random amount of grinds into the filter and hope for the best.

Copyright

CC BY-SA 4.0 Deed