A show devoted entirely to numbers (and letters)

 

A very good quiz show began screening recently on SBS. Letters and Numbers is a local incarnation of the French Les Chiffres et Des Lettres, which started in 1965 and is still going strong.

The SBS version hasn't received a lot of press, perhaps because the prizes are not exactly humongous: an alternative title for the show might be Who Wants to Win a Dictionary? Nonetheless, for fans of Scrabble and arithmetic (and your Maths Masters are both), the show is a lot of fun.

In fact, one of your Maths Masters auditioned to be a contestant. He is now waiting for his turn, having been officially categorised as back-up cannon fodder. Notably, it was his numbers rather than his letters that let him down.

This was, to say the least, surprising and annoying. What, with all nearby calculators smashed and useless, he gets lots of practice with mental arithmetic, and he likes to think he's pretty quick. But, demonstrably not quick enough.

The numbers challenge in the show involves the "small numbers", from 1 to 10, together with the "large numbers" 25, 50, 75 and 100. Six of these numbers are then chosen randomly, and the challenge is to use some or all of these numbers, together with the basic operations of arithmetic (+, −, ×, and /), to reach a target number. You are given 30 seconds to do so.

For example, the picture above shows the show's "maths guru", Lily Serna, preparing to use the six numbers 75, 50, 9, 8, 4, 4 to reach the target of 729. And, one solution for this challenge target is

How does one get good at this? Clearly practice is important, and there are a number of helpful online sites: a good one is here. Indeed, after his humbling audition, your Maths Master decided to practise, and quickly picked up speed. But, it needs more than practice to become a numbers wiz. Strategies are key.

One strategy that often seems to work well is to think in terms of hundreds. Suppose, for example, that our random numbers are the same as Lily's and the target number is 529. That's five hundreds, and we can get very close to our target with another 25. So, we look to make (20 + 1) × 25 = 525. We can actually get this, since 75 − 50 = 25 and 4 + 8 + 9 = 21. That gets us 4 off the target, but we have a second 4: a complete solution is then

 

That may seem a little lucky, and you do have to calculate quickly. But with all the arithmetic operations at play, a surprisingly large number of targets can be hit quite easily.

Having practised, your Maths Master then joined the studio audience, to see the show in action. He was reassured to find that he was quicker and more accurate than the contestants (admittedly without the great nervousness of being on national television). But there was also Lily.

Lily can beat your Maths Master hands down. She was clearly much quicker and much more inventive in her solutions. This was really annoying. It was time for Lily and your Maths Master to have a little chat.

Needless to say, Lily is charming. When not being the maths guru on Letters and Numbers, Lily is working on her honours research at the University of Technology, Sydney. Her thesis is on the modeling of pollutant flow in the Great Barrier Reef. It is obviously important work, and it is work that Lily is clearly passionate about.

And what about Lily's skill at the numbers challenge? Surprisingly, Lily said her mental arithmetic was not that strong when the show first came about. However, she practised hard, and she devised a number of different strategies to apply. Lily has become astonishingly quick at applying them.

Lily also indicated one clear trick that really helps: she has learned her 75 times table off by heart. This gives her easy access to numbers where thinking in hundreds will be much clumsier. For example, the target of 729 above would be a struggle for your Maths Master, but is a cinch for Lily.

There are actually some very sharp contestants on Letters and Numbers. So, does Lily ever get bested? She paused, and smiled: "Rarely".

Puzzle to Ponder: Feel free to suggest solutions in the comments section. Please also email us if you wish to be added to our email list.

Using the numbers chosen for Lily above, can you make all the targets 29, 129, 229, 329, ... 929? What if the chosen numbers were 1, 3, 9, 25, 75, 100: what would be the smallest target number, from 1 to 999, that you cannot hit.

Letters and Numbers screens at 6:00 pm weeknights, on SBS ONE.

The Maths Masters will also be appearing on the television show Scope, on Channel 10 at 9am this coming Saturday.

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