A 10-PART SERIES · AUSSIE SCIENCE CLIPS
Mathematics Puzzles
Ideas so simple a child can ask them, that took humanity centuries to crack. Each episode starts with an apparently small puzzle and ends by changing what the viewer thinks a number means.
EPISODE 1 · 12 min
What is zero, and why did it take so long to invent?
Here's a puzzle. Write a 2 and a 5 side by side, and you've got 25. Now slip a little circle in between them, and you've got 205. You added nothing, and the number went up by 180. So how can nothing be worth a hundred…
EPISODE 2 · 12 min
What is infinity, and can one infinity be bigger than another?
Here's a puzzle. Which are there more of: the counting numbers, one, two, three, forever, or the square numbers, one, four, nine, sixteen? Surely the counting numbers, because most of them aren't squares. But pair them…
EPISODE 3 · 11 min
Does 0.999… really equal 1?
Here's a puzzle. Write zero, a decimal point, and then nines, forever. Zero point nine recurring. Is that equal to one, or just a little bit less than one? Most people's gut says less. Hold on to your answer, because…
EPISODE 4 · 11 min
Should you switch doors?
You're on a game show, facing three closed doors. Behind one is a car, and behind the other two, goats. You pick door one. The host, who knows where the car is, opens door three: a goat. Do you want to switch to door…
EPISODE 5 · 11 min
Why do 23 people probably share a birthday?
Here's a bet. Walk into a room of 23 people, chosen at random, and offer even money that two of them share a birthday. Not your birthday, just any two people, same day and month. With 365 days to choose from, it sounds…
EPISODE 6 · 12 min
Why do prime numbers keep your bank account safe?
Last time we ended on a lock anyone can check but only you can close. To see how it works, start with a puzzle in two halves. First: what's 47 times 59? With a pencil, you'll have 2773 inside a minute. Second: two…
EPISODE 7 · 12 min
Why does pi never end?
Here's a puzzle you can do in the kitchen. Wrap a string once around a jar lid, then lay it straight across. It goes across three times, with a little left over. A coin or a bike wheel: three, and a bit. That bit…
EPISODE 8 · 11 min
How did Achilles ever catch the tortoise?
Here's a puzzle. Achilles, the fastest runner in Greek legend, races a tortoise and gives it a head start. Before he can pass it, he has to reach the spot where the tortoise started. But by then the tortoise has…
EPISODE 9 · 11 min
How did seven bridges start the maths behind Google Maps?
Here's a puzzle. A river splits around an island, and seven bridges join the island, the two banks and a piece of land to the east. Can you go for a walk that crosses every bridge exactly once? Start anywhere, finish…
EPISODE 10 · 12 min
Can maths prove everything?
Here's a puzzle. Read this sentence: this sentence is false. Is it true? If it's true, then what it says holds, so it's false. But if it's false, then what it says is right, so it's true. It flips forever and never…