When I was six, my sister was half my age. Now I’m 70, how old is she?

If you spend much time on social media, there’s one of these fun questions you might get asked sometimes: When I was six, my sister was half my age. Now I’m 70, how old is she?

This isn’t actually a deep philosophical question, but rather a simple maths sum. Let’s figure this out.

When I was six, my sister was half my age. Now I’m 70, how old is she. Your sister is three years younger than you, so now that you’re 70, she is 67.

So, when you’re six, your sister is half your age, which is 3. Your sister is 3 years younger than you are. When you turn 70, your sister is still 3 years younger than you are, and therefore she is 67. Let’s turn that into a maths sum where Y is your age an S is your sister’s age.

S= Y-(6/2)
Y= 70
Therefore
S=70-(6/2)=70-3=67.

The Wrong Answer

A widespread mistake that some people are going to make is assuming that because the speaker’s sister was half his age at one point in his life, that must mean that she is going to be half his age for the rest of their lives.

Anyone who knows anything about time will soon realise that this isn’t the case. But often, when you word questions in a particular way, our common sense goes out the window. I’ve heard way too many people telling me that answer to this question is 35.

Is it even a riddle?

What’s interesting about this kind of riddle is that I’m not too sure if it even qualifies are a riddle.

Google describes a riddle as “a question or statement intentionally phrased to require ingenuity in ascertaining its answer or meaning.” And if we are taking this definition at face value, then it might be hard to argue that it’s not a riddle.

It’s a question, and we need to think a bit deeper than we usually would do when trying to find the correct answer.

Is it just a maths question?

However, some would argue that it’s not a riddle; it’s a maths problem.

As we demonstrated in the introduction, you can remove all the words and turn it into an algebra question. Doing so makes it become the sort of thing that most people who passed high school maths will be able to answer.

If the question where to be put on a maths quiz, it might be phrased as
“1. What is half of six?
 2. What is 70- your answer to question one?”

However, the addition of talking about age could confuse some people and make them not even consider the pure mathematics behind it.

What’s the point in this kind of question?

You might call this type of riddle a “Maths Riddle”- A kind of riddle that is essentially just a maths sum but phrased in a way that makes it harder to get to the correct answer.

Maths riddles are great for people with interest in mathematics, but also for people who wish to explore how our use of language can affect the way we view the world. How when you use language in particular ways, it can even trick us into going into all sorts of thought patterns that aren’t needed.

What sort of word is “half”?

The sort of language that we use in mathematics can also be a powerful insight into how we use language to explore the world through maths.
In this particular scenario, there are two arguments for what sort of word “half is”.

Some people would argue that it’s a Predeterminer/Adjective because it’s being used to describe something, someone’s age.

However, you could also make the case that’s it’s an abstract noun- a noun that you can’t physically touch such as joy. People who think this would argue that half is an abstract thing, just like all other numbers.

Sister’s Perspective

If you wanted to, you could rephrase the riddle so that it’s from the sister’s point of view. By doing this, you will still be exploring how the manipulation of the English language can affect the way we think about mathematics.

“When I was 3, my brother was twice my age. Now I’m 67, how old is he?”

Some people might say her brother must now be 134. However, let’s look at this by analysing the maths.

Double three is 6. And six minus three is three.
 She is three years younger than her brother.
Now that she is 67, and her brother is three years older, that makes him 67.

Maths riddles

Maths riddles are a brilliant type of riddle because they blur the line between a riddle and a maths sum. They’re not the type of problems that have something you can just type into a calculator.

Well, they do. But the real challenge is figuring out what you need to type in to get the right answer, making it more attuned to how maths works in the real world.

In the classroom, your teacher will usually just tell you the sums and tell you how to figure them out. However, in the real world, you’ll need to figure out the sums using the information you’ve been given.

Not to mention, they’re also super fun.

Examples

Let’s take a look at some other maths riddles and try to figure out the answer.

“In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?”

This one is great because it combines three different school subjects, English, Maths, and History. The answer to this one is simply that he was born in BC, not AD.

“In two years, I know, I’ll be twice as old as five years ago, said Tom. How old is Tom?”

Let’s say that Tom’s age is T.

T + 2 = 2(T – 5)
T + 2 = 2T – 10
12 = T

“What is half of two plus two?”

For this one, you need to know about BI(DM)(AS), the way of knowing in what order to do a sum. If we were to write the question as a sum, it would be.

2/2+2

BI(DM)(AS) means that we need to divide the addition, so the sum becomes

1+2, which is three.

Conclusion

At first glance “When I was six, my sister was half my age” might seem like a fun way to trick people, but it’s a maths riddle. Maths riddles are an effective way of demonstrating how people can use the English language to alter how we approach mathematics.

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