I made the lowest possible winning score for a completed frame of snooker, potting only one ball in the...

competition/games/snooker New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

I made the lowest possible winning score for a completed frame of
snooker, potting only one ball in the process; what colour was it?

[ Editor: the title sentence above is a summary; the original puzzle
  follows. ]

Here's one in honour of the World Professional Snooker Championship
(currently in progress in Sheffield).  You'll need to know the rules of
the game.

I played an unusual game of snooker the other day - in fact, I made the
lowest possible winning score for a completed frame.  Not only that, I
only potted one ball in the process!

What colour was it?

-- Bob Newman <yaw74@dial.pipex.com>

Show solution

Blue.

In his opening shot [Editor: "openingsshot" in the original], your
opponent manages to pot all 15 reds and yellow.  That's a foul, so you get 4 points, but the reds are gone.
Then your opponent pots yellow, green and brown.  You pot blue, your
opponent pink.  The score is 15 - 9.  Then he makes a foul on the black,
giving you 7 points, and that's the end of the frame, with a 16 - 15
victory for you.

-- Abigail <abigail@fnx.com>

[ Editor: from the same thread, "Snooker Puzzle - Spoiler", January
1998, on the claim that a break of 2 is the hardest break to make. ]

ejr <ejr@indigo.ie> wrote:
> A break of 2 is the most difficult to achieve on the snooker table as it
> can be made only by potting the yellow when all the reds have been cleared.
> There is no other way of making a break of 2.

Abigail wrote:
> Actually, if you have a free ball with no reds and 6 colours left,
> you have 6 ways of making a break of 2. But this doesn't make a
> break of 2 not the most difficult.

You can also make a break of 2 by potting two reds in the same shot
(and then missing the colour, of course).

-- Steve Thomas <Steve.Thomas@insignia.co.uk>

[ Editor: the original puzzle and spoiler of the January 1998 thread
"Snooker Puzzle", quoted only in part above. ]

Here is a puzzle for all those snooker fans.

Mathematically, what is the most difficult break to achieve in snooker.
The obvious answer of 147 is not correct as there are 15 factorial ways
of making a maximum break assuming the reds can be pocketed in any
order.

Any takers?

Spoiler.

A break of 2 is the most difficult to achieve on the snooker table as
it can be made only by potting the yellow when all the reds have been
cleared.  There is no other way of making a break of 2.  Any other
break can be achieved by various combinations of reds and colours.  In
fact, there are a total of 1307674368000 different ways of achieving
the magical 147.  So simple really.

-- ejr <ejr@indigo.ie>