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How to Solve the Famous Coffee and Cream Puzzle

Summer is brain-teaser season in my house. And since summer has now officially arrived, it’s officially brain-teaser season for The Math Dude. What’s the puzzle for today? Keep on reading to find out!

By
Jason Marshall, PhD,
June 24, 2016
Episode #283

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Latte ArtOver the past few weeks, summer decided to make its grand entrance for the year here in Los Angeles. By which I mean to say that it’s been hot. And I don’t just mean kind of mildly toasty hot, I mean super duper unpleasantly hot—so hot that you don’t want to step outside during the day (or even night) hot.

While this forced indoor isolation is kind of a bummer, I’m a glass-half-full kind of guy so I prefer to see it as an opportunity to do one of my favorite things—sit indoors in an air-conditioned coffee shop and think about math. In particular, I’ve been digging around the internet looking for great new brain-teaser puzzles. And I’ve found a bunch—one of which, I’d like to share with you today.

So, without further ado, let’s begin teasing our brains.

The Coffee and Cream Problem

Imagine that you and I are sitting together at a table in a nice and cool coffee shop escaping the summertime heat. A waiter approaches the table and carefully sets a single cup of coffee and a pitcher of cream down. He says that each container is filled with exactly 10 ounces of liquid. At this point in such a story, most normal people living in a normal world filled with normal situations would pour a dabble of cream in their coffee and get on with the show.

Here’s a puzzle for you to ponder …

But this is not a normal coffee shop and the waiter doesn’t walk away. Instead, he sets down a spoon which holds exactly 1 ounce of liquid, and says:

"Here’s a puzzle for you to ponder. If you put a spoonful of cream in your coffee and then put a spoonful of creamy coffee back in your cream, will there be more cream in your coffee or more coffee in your cream?"

At this point, we both look up at the waiter with utter confusion on our faces. And then we notice who he is, and it all makes sense. The waiter is none other than Charles Dodgson, the English mathematician and writer that you probably know as Lewis Carroll (of Alice in Wonderland fame).

Many people don’t know it, but Carroll was actually first-and-foremost a mathematician and logician, and this is one of the puzzles with which he loved to tease his friends’ brains.

So, my friends, I now use it to tease your brains. Take a few minutes, think about it, and then when you’re ready, continue on for the answer.

How to Solve the Puzzle

As with every good puzzle, there are multiple ways to arrive at an answer to today’s brain-teaser. Of course, there’s only one actual answer, but there are multiple roads you may travel along to arrive at it. To show you what I mean, we’re going to think about today’s puzzle in two different ways.

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