Number 18: Solve a classic brain buster to win a prize

Plus the mathematical beauty of the James Webb telescope, and did you know that Catch-22 was almost named Catch-18?

Solve this classic brain buster to win a prize

Time for you to be tormented by a famous mathematics problem that has given many people headaches over the years – including me when I first saw it.

Anisha, Ben, Cassie and Dong need to cross a rickety old wooden bridge between two mountain tops late at night (don’t ask why, that’s not important!)

They only have one very weak torch, which means only two of them can cross at any time. In addition, when two people cross together, they must travel at the slower person’s pace so they can both see. This also means that one person must return each time with the torch.

To top things off, in exactly 18 minutes the bridge will collapse (again, don’t ask why, that’s not important!).

Anisha can get across the bridge in 1 minute, Ben in 2 minutes, Cassie takes 5 minutes and Dong 10.

When Anisha and Dong go across, that takes 10 minutes and Anisha returns with the torch taking 1 minute. Anisha and Cassie then cross and Anisha returns again, taking 5 minutes plus 1 minute. Anisha and Ben then cross together in 2 minutes.

In total, that takes 10 + 1 + 5 + 1 + 2 = 19 minutes and just about anyone you ask comes up with that as the quickest possible crossing time. Like I said I certainly did when I first saw the problem.

But in fact, they can get all across the bridge quicker than that!!!

Find a combination of crossings that gets Anisha, Ben, Cassie and Dong safely across the river in less than 18 minutes.

And I know what you’re thinking – there’s no ‘trick’ involving three people crossing at once or anything like that. Only two people can cross and one must return to accompany another, but with the right combination of people it can be done faster than my example above. Honest!

Send your solution to number@adamspencer.com.au to go in the running for a signed copy of one of my books. Deadline for entries is Monday 13 November 11pm AEDT.

Mirror mirror - the James Webb telescope

Launched on Christmas Day 2022, the James Webb telescope has sent some incredible images back to Earth, expanding our understanding of the cosmos. And it is all thanks to the mirror on the telescope, which is the largest and most powerful ever built.

Truly a marvel of engineering, the telescope is comprised of 18 hexagonal segments, each made of beryllium coated in gold. These materials combine to create a mirror that is unparalleled in collecting light.

The mirror segments are arranged in a honeycomb pattern with each one aligned to within a fraction of a human hair, which is essential for the telescope to focus properly.

The hexagons are each 1.32 metres in diameter and weigh approximately 20 kilograms. The total diameter of Webb's primary mirror spans 6.5 metres.

Fascinating facts about 18!

Almost Catch-18?

Joseph Heller’s famous novel Catch-22 was changed from the title Catch-18 for fear of confusion with Leon Uris’ war novel Mila 18. Heller and editor Robert Gottlieb vetoed 11 (Ocean's Eleven got there first), 14 ("an unfunny number") and 26 which just didn't feel right. One night Gottlieb simply decided that Catch-22 was funnier than 18 and a famous English phrase came into being.

Cute cube

Here's a beautifully obscure and cute mathematical fact about the number 18:

Cheap street

Recently in Melbourne, I spotted a short street named ‘Eighteen Pence Lane’ (also home to an excellent coffee shop of the same name!) Why ‘Eighteen Pence’ Lane? The best (ideally accurate) explanation will win a signed copy of one of my books. Leave your answer here. I’ll do the same for the nearby equally awesomely named ‘Swinging Basin Lane’!!!

Suosikki sanaani suomeksi*

If you can speak a bit of Finnish, you don’t need me to tell you that the word ‘hyppytyyny’ means ‘bouncy cushion’. Half of this entire, awesome, very specific word is made up of the letter ‘y’!

So now brace yourself for 18 letters of pure joy: hyppytyynytyydytys.

Gorgeous.

Oh, what does it mean? ‘Bouncy cushion satisfaction’.

May your day be full of hyppytyynytyydytys.

*Translation: "My favourite word in Finnish"

The truncated tetrahedron

Take a pyramid with a triangular base (otherwise known as a tetrahedron – ‘tetra’ meaning four in Greek, ‘hedron’ meaning face in ancient Greek).

Now truncate (cut off) a pyramid from each corner.

You get a ‘truncated tetrahedron’ and you should be able to count 18 edges.

It also has 8 faces and 12 vertices (or corners).

As such it obeys the famous “Euler’s Formula” V + F - E = 2.

Convince yourself this amazing geometric observation works on a cube, a triangular-based pyramid, a square-based pyramid, and any other ‘polyhedra’ you might like.