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Sudoku -

Sudoku

Mathematician and comedian, Simon Pampena, reveals the number of clues needed to make a Sudoku
truly unique.

TRANSCRIPT

Simon Pampena

If you're a Sudoku devotee like me you may have been stumped by a puzzle once or twice, and let fly
with. 'There's not enough clues, this Sudoku must be unsolvable.' But who's wrong? You or the
Sudoku? Well new research has uncovered the minimum number of clues a Sudoku player needs to have
any chance of solving a puzzle. And the technique they use might just improve your mobile phone
reception. But we'll get to that later. First, here's how a Sudoku works. Starting with nine, three
by three boxes, your challenge is to fill empty squares with only the numbers one through to nine.
Now you're always given clues to start with, and from those clues you must deduce every other
number in the grid. But you can only ever put a number once in every row, once in every column and
once in every three-by-three box. Now, the less clues you're given, the more difficult your Sudoku
is likely to be. But there are limits. And that's because every Sudoku needs to be unique - only
one solution. If you were to try doing a Sudoku just with one clue, you could end up with enough
solutions to cover half the surface area of the sun.

NARRATION

So what's the minimum number of clues that can offer up just one solution? Well a team from
University College Dublin recently applied their mathematical wizardry to solving the problem. And
the magic number is seventeen.

Simon Pampena

Now while Sudoku lovers were obviously overjoyed to hear this news, there are parallels for modern
communication. Every time you use a mobile phone, you're reliant on Sudoku-type error checking and

NARRATION

It works like this. When you make a call, software encodes your voice into a digital signal of
zeroes and ones. This binary stream is sent to the person you're calling. Their phone transforms
the signal back into analogue, and you should hear the person's voice on the other side.
Theoretically. In practice ...

Simon Pampena

Hello? Hello?

NARRATION

... bits of the digital information are lost in transmission. So you end up with a problem similar to
a scratched CD - unreadable data.

Simon Pampena

Oh, hello? Hello? The way around this is to send the original information in bigger blocks.

NARRATION

A piece of information is transmitted essentially as a completed Sudoku grid. Then while the signal
is flying through the air, bits are knocked out randomly, and your phone receives an incomplete
Sudoku. But there's a chip in your phone that can quickly fill in the Sudoku, and thus retrieve the
missing data that is your voice. Obviously there are still limits.

Simon Pampena

But these limitations are being improved all the time, and just like the discovery of the minimum
Sudoku, mathematicians can figure out how much data you can lose before you lose your connection.

Hello? Hello? Hello?