Sep 20, 2023

Number 17: From haikus to subs and sudokus

An English haiku Has seventeen syllables Flowing through three lines

And a free SXSW event with Dr Karl and me on 21 October in Sydney

Solvable Sudokus

Number puzzles first started appearing in newspapers in the late 19th century. French puzzle setters began experimenting with removing numbers from magic squares, but the phenomenon known as ‘Sudoku’ only exploded in popularity in the 2000s.

As most know, the aim of a Sudoku is to place the numbers 1 to 9 in every row, column and 3x3 square of a grid as shown above – with no repetition in any row, column or 3x3 square. The puzzle begins with some squares filled in – typically around 25 of them. For any puzzle you are given, there is only one answer.

For Sudoku players, it is obvious that you cannot solve the puzzle on top left because you simply don’t have enough information. There must be millions of different solutions with a seven in the middle. Similarly, there is so much information given to you in the puzzle on the top right, that there is obviously only one, unique, solution to the grid.

So the question that leaps into any mathematician’s mind … what is the least number of clues needed for a Sudoku to be uniquely solvable? Well in 2012 Gary McGuire, Bastian Tugemann and Gilles Civario proved this answer to be 17! Yep, turns out there is no solvable 16-clue Sudoku.

SXSW free event!

I’m honoured to be hosting several sessions at South by South West (SXSW) Sydney, bringing together inspired thinkers, creators and innovators from across the world.

Alongside the paid program runs some awesome free events, and I’m thrilled to announce that I’ll be on stage with the one and only Dr Karl **FREE** on Saturday October 21.

This is the first time SXSW has left its home in Austin, Texas. Come and get your geek on in Sydney with a true national treasure. Details here

Just a regular heptadecagon

Since ancient times mathematicians have been fascinated with what we call ‘regular” polygons, or shapes. Regular means that every side is the same length, such as equilateral triangles and squares.

The Greeks absolutely loved regular polygons that could be constructed with a compass and an unmarked straight line. For example, if you draw a circle with a compass and keeping the compass at the same size then draw two internal arcs (as shown below), these 6 points will form a regular hexagon.

Think that’s cool? Well in 1796 the great German mathematician Carl Friedrich Gauss figured out how to construct a heptadecagon (a figure with 17 equal sides) using this same compass and straight line method.

I’m not sure what was more impressive – that he did this while a teenager, or that he did it one morning while lying in bed!

Fascinating facts about 17!

Taste of a [nuclear] generation

In 1989 PepsiCo Inc acquired 17 nuclear submarines from the Soviet Union. Urban legend says this multinational briefly owned the 6th largest fleet in the world. In truth, these subs were old, obsolete warships that PepsiCo delivered to a scrapheap in Norway in return for being allowed to sell their soft drinks in Moscow. Read the full story here

Beware the ‘Soft 17'

In a hand of blackjack or 21, the dealer must keep drawing until their hand totals at least 17. In SOME casinos, if the dealer has a ‘Soft 17’, that is, a score of 17 involving an ace, they must draw again. So best you check which house rules apply before you start mouthing off!

Trick 17

If a German friend ever describes something as a “Trick 17” they mean that it is a simple, original and ingenious solution to a problem; perhaps what we might call a lifehack. Where the 17 comes from in Trick 17, hmmm - I’m not sure. And I’ve got even less idea why the Swiss say Trick 77.

Prime sum

There are many prime numbers that are:

The sum of 3 successive primes e.g. 5 + 7 + 11 = 23, 11 + 13 + 17 = 41.
And 5 successive primes e.g. 11 + 13 + 17 + 19 + 23 = 83 or 31 + 37 + 41 + 43 + 47 = 199.

However, there is only one prime number that is the sum of 4 successive primes. You guessed it: 17 = 2 + 3 + 5 + 7.

Wallpaper groups

Also known as a plane symmetry group or special tessellation, wallpaper groups are a type of 2-dimensional repetitive pattern, based on the symmetries in the pattern.

Such patterns occur frequently in architecture and decorative art. There are 17 distinct wallpaper groups.

So while you might look at these triangles and hexagons and think, ‘wow cool pattern’, a mathematician will see it and say, ‘ah the wallpaper group p6m’. Yeah, we’re a bit different!

Image credit: Artlandia