What is an even number?

0:47 Welcome to Maths Is Not Boring by Kidopoly.com. I'm Mira. And I'm Finn. If you haven't already, tap follow wherever you're listening so you never miss an episode.

0:59 Hey Mira, I was just looking at the tiles on the kitchen floor and I started counting them in my head. I just love picturing how big numbers can get. Like a million or a billion or even a trillion.

1:12 Oh, I love doing that too. And you know, Finn, there is a secret hiding inside every single number, no matter how gigantic it is. Have you ever noticed that the way houses are arranged on a long street is exactly the same as sharing out a big bag of sweets with your friends?

1:31 Wait, what? Houses are made of bricks and concrete, not sweets. And how on earth does a bag of sweets connect to a gigantic number stretching across the universe?

1:42 It is completely connected. Today we are looking at something so simple you probably already know it by heart. But it is actually the oldest pattern in numbers.

1:54 The oldest pattern? Like older than castles and dinosaurs?

1:59 Well, older than almost anything humans have written down about math. And this seemingly simple pattern has secrets hiding inside it that literally change how you see the world. Once you see it, you will spot it secretly organising everything around you. We are talking about odd and even numbers.

2:19 Oh, I know those. Two, four, six, eight are even. One, three, five, seven are odd.

2:28 Exactly. But let's look at what that actually means in the real world. Forget the math symbols for a second. Picture lining up a huge handful of your favourite sweets.

2:39 Ooh, okay. I'm picturing little green and red jelly beans. I have a massive pile of them. Perfect.

2:46 Now, start sliding them across the table in pairs. Two for you, two for me. Two, two, two.

2:53 Alright, I'm lining them up. They look like little cars in traffic.

2:57 If every single suite gets a partner and there is absolutely nothing left over, that number is even. But if you pair them all up and there is one lonely suite left sitting by itself.

3:10 Then it's odd! It's the odd one out. That one suite just has to sit there looking at all the happy pairs.

3:16 That is the whole difference between even and odd. Either every suite has a partner, or one is left over. And people have been staring at this exact pattern for a very, very long time.

3:29 How long exactly?

3:30 About 2,500 years ago in ancient Greece. A group of thinkers called the Pythagoreans were among the first to actually write this down.

3:40 2,500 years? That is ancient. People were playing with Odd and E back then. They were obsessed with it.

3:48 The Pythagoreans gave numbers personalities, almost like characters in a story. They believed the odd and even were the two basic forces of the entire universe.

3:59 Wait, personalities? Like, hello, I'm number four. I'm very tidy and polite. Kind of.

4:07 They actually believed that the number one wasn't really a number at all. They thought one was just the source, the builder that created all the other numbers.

4:16 Hold on, one isn't a number. That's crazy! If I have one jelly bean, I'm definitely counting it.

4:24 It was just their belief, not a mathematical fact. But it shows how deeply they thought about what numbers actually mean, not just how to count with them. Because they stared at this pattern so closely, they found surprises hiding inside it. Surprises we still use today. Let's go back to our jelly beans.

4:43 Okay, my jelly beans are back on the table.

4:46 Picture a pile of odd sweets. Remember, that means when you pair them up, there is one lonely sweet left over.

4:54 Got it. Poor lonely jelly bean, just sitting there at the end of the line.

4:59 Now, close your eyes and picture a second pile of odd sweets. That pile also has one lonely suite left over.

5:07 Okay, two separate piles. Each one has a lonely suite.

5:12 What happens if you push those two odd piles together into one giant pile?

5:18 Let me picture it. Wait, the two lonely suites. Because you push the piles together, they find each other.

5:25 They become a pair. Exactly. Add two odd numbers together, and you always, always get an even one. Because the two lonely suites pair up with each other.

5:37 That is so cool! I can literally see it happening in my head. I didn't even have to do any math or use any times tables. It just happens naturally.

5:47 That's the beauty of it. And the most amazing thing is that this pattern holds for every number, however big. Even ones nobody has ever written down in the history of the universe.

5:59 Like a number that's a trillion zillion digits long. So big it stretches all the way to Jupiter.

6:06 Yes, if you have a number that stretches to Jupiter, you don't have to work out the whole thing. Just look at the very last digit. If that last digit is even, the entire giant number is even.

6:19 Because you already know if the very last suite has a partner or not. That is a serious shortcut. Okay, but hold on. If odd plus odd is always even, and you just look at the last digit, what about the strangest number of all? What about zero? Ah, the big question. Is zero odd or is it even? I feel like a lot of grown-ups would say it's neither.

6:44 Because zero is just nothing. You can't put nothing into pairs. It's like having an empty table.

6:52 Many grown-ups do hesitate. It feels strange to think about nothing having a pattern. But a professor of mathematics would insist, without a doubt, zero is even.

7:04 Wait, really? How can nothing be even? That sounds like a trick.

7:09 Let's test it using our sweet rule. Remember, an even number means nothing is left over when you split it into two equal groups.

7:18 Right. If I have six sweets, I can make two groups of three, and none are left over.

7:24 So, if you have zero sweets, you split them into two equal groups of zero.

7:31 And are any sweets left over?

7:33 No, nothing is left over. You started with zero, you split it in half, and you still have zero. Nothing is left out.

7:43 Whoa, so it totally follows the rule.

7:46 Exactly. Plus, think about how the numbers sit in a line. You have the odd number, negative one, then zero, then the odd number, positive one. Zero sits perfectly between two odd numbers, exactly where an even number has to be.

8:03 That completely makes sense. Zero is just sitting there doing its job, being an even number, and most people don't even realise it. So zero is officially an even number. That actually makes the whole pattern feel complete, stretching backward and forward forever.

8:21 It really does. And this pattern isn't just invisible math floating in space. It decides things in your life every single day.

8:30 Like what? I don't see floating jelly beans when I walk outside.

8:35 Think about where you live. When you walk down a street, the houses on one side are often all odd numbers, and the houses on the other side are all even numbers.

8:45 Oh, I see it. Like 1, 3, 5 on the left side and 2, 4, 6 on the right side. That is the sideways connection you were talking about at the start.

8:57 Exactly. City planners use odd and even to organise our streets so the postman knows exactly where to go. And think about games. How do you decide who goes first in a lot of games? You use chance, right? Like flipping a coin, picking a card, or rolling a dice.

9:16 Oh, a standard dice goes up to six. That means it has exactly three even numbers and exactly three odd numbers. Which means what? So if you pick even, you have the exact same chance of going first as if you pick odd. It's totally perfectly fair.

9:34 Right. The oldest pattern in numbers is quietly organising our streets and making sure our games are perfectly fair every single time.

9:44 I am never going to look at a street sign or a dice the same way again. It's like the universe is just constantly sorting jelly beans.

9:52 Alright, Finn, it is time for the quiz. Let's see if you can remember the secrets of the oldest pattern in numbers.

10:00 Okay, I'm ready. My brain is totally tuned in. Let's do this. First question.

10:07 What group of ancient Greek thinkers were among the first to write down the rules of odd and even? Next one. About how many years ago did those Greek thinkers live? Question three. What kind of number do you get if you add an odd number and an odd number together? Here's number four. According to a mathematics professor, is the number zero odd or even?

10:46 Last question. The ancient Greeks gave numbers personalities and they believed a certain number wasn't actually a number at all. Which number was it? Great job! Let's go through the answers and see how you did. The first answer is the Pythagoreans, they were obsessed with this pattern. For question two, they lived about 2500 years ago in ancient Greece.

11:18 Number three, the answer is you always get an even number, because the two lonely suites find each other and pair up. Question four. Zero is absolutely an even number because nothing is left over. And the final answer is, they believed the number one wasn't a number, just the builder of all the others.

11:41 It is completely wild to me that a pattern from 2500 years ago is still deciding which side of the street we live on today.

11:51 And it will keep doing it forever. Every time you roll a dice, or check a house number, or pair up your snacks, you are part of that ancient pattern.

12:01 If you liked exploring odd and even with us, we'd love it if you could leave us a five-star review. The Pythagoreans would definitely give this episode five stars. Just scroll down on your app and tap the stars.

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12:44 Keep looking for those hidden patterns. See you next time on Maths Is Not Boring.