My biggest maths lesson

Coffee with milk

The most important maths lesson in my life wasn't actually that hard. It wasn't even really about maths.

Back in the primary school we had the following problem to solve:

There's a guy who likes his coffee... strange. He gets a cup of black coffee, drinks half of it, then fills the empty half of the cup with milk. Drinks half of it and fills back up with milk. His coffee gets whiter and whiter that way, until after the eighth time he just drinks it whole. How much coffee and how much milk did he drink overall?

We've spent the entire lesson calculating this shit. An entire class of primary school kids trying not to make a mistake in their fractions. And not just regular kids – it was an extracurricular for pupils gifted at maths.

At first he drank ½ a cup of coffee. Then he drank a half of this half-coffee half-milk mixture. So now it's ½ + ½⋅½ = ¾ cup of coffee, and ½⋅½ = ¼ cup of milk. Then he drank a half of the ¼-coffee ¼-milk mixture, or something... Then five more times...

Our young brains, that had just learned about fractions in the first place, were now melting, basically trying to calculate the 8th power of some messy fractions. Everyone got a different result. We were tired, disappointed and ready to give up.

So then the teacher gave us the answer. It's one cup of coffee and 4 cups of milk. Simple as that. Not 507/512 cups of coffee and 1034/256 cups of milk, or whatever we came up with.

Why were we so wrong and tired, while she managed to calculate the correct result in her head in a second?

Because we were calculating how much he drank (exactly what the question was), while she calculated... how much he poured into the cup. He drank everything he had poured, so why not?

He poured in a full cup of coffee and 8× half of cup of milk, and then drank it in an overcomplicated way. That's it.

So here's my math lesson: if you're stuck solving a problem (any problem, not just primary school maths problems), but it gets increasingly harder and harder to solve – don't keep plowing like an idiot, and stop being so sure you're gonna solve it if only you just work hard enough. Instead, take a step back, take a deep breath and try to find a totally different way around it.

Sometimes it's way better to work smart than hard.

The whole class (including the teacher who kept pretending to help us all along) has spent an entire hour calculating boring and complex stuff, while we could have just spent a minute to think about it first.

We didn't waste that hour. It might have been one of the most valuable hours of my early life.

A photo of me

About the author

Hi! I'm Andrea (they/them). I tell computers what to do, both for a living and for fun, I'm also into blogging, writing and photography. I'm trying to make the world just a little bit better: more inclusive, more rational and more just.