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One for the mathematicians out there...

Community Veteran
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Registered: 30-08-2007

One for the mathematicians out there...

I know we have a couple of mathematicians who like to have a go at "impossible" theory's.
I'm an interested, fairly regular but not fanatical watcher of TV snooker, and wondered how many combinations of post-break ball layouts there are, or if indeed it is an impossible question to answer.
The professional table is 6ft x 12ft (1.8m x 3.7m)
The professional ball is 2 1/16" in diameter (52.5mm)
Which gives slightly over 2272 full sized circles on the table, but of course balls don't always conveniently come to rest exactly in a full space.
15 reds, 1 of each yellow, green, brown, blue, pink and black. And of course the white.
Which are pretty much the only constants.
Lets be kind and say a player pots (unlikely but not impossible) a red off the break and competes a 147 unbroken break, 1 red will be removed at each odd numbered stroke of the cue followed by a colour on the even strokes.but this colour will be replaced on its starting spot until after all the reds are potted, after that the colours will go consecutively and not replaced.
Experience; is something you gain, just after you needed it most.

When faced with two choices, simply toss a coin. It works not because it settles the question for you. But because in that brief moment while the coin is in the air. You suddenly know what you are hoping for.
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Community Veteran
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Registered: 06-02-2008

Re: One for the mathematicians out there...

The number of potential ball positions is 2272^n where n = number of balls on the table. It would be elegant if the solution was 2272^n! but this isn't quite how the game is played, Google says that 36 shots are required for a max break, making the total 6.7717E+120.
However, it's been a decade since I had any formal statistics tuition and I may well be wrong Smiley ... you also need to decide whether to count the 'interim' position when the colour is replaced after being potted - my solution does not count this,
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Re: One for the mathematicians out there...

Quote from: Petlew
I know we have a couple of mathematicians who like to have a go at "impossible" theory's.
I'm an interested, fairly regular but not fanatical watcher of TV snooker,

And if you are not fanatical about it...what sort of questions would you come out with, if you were  ? ?    Sad
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Re: One for the mathematicians out there...

deleted... double posted the comment, due to "waiting for plusnet"....  Undecided
Community Veteran
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Re: One for the mathematicians out there...

@shutter, Throughout my life I've been an avid collector of party pooping useless information, which apart from a brain stretching exercise for mathematicians, this is.
Oh yes, thank you Ben Trimble. Next time somebody asks that question, I shall be able provide an educated answer....
Unless someone has a better answer of course Smiley
Experience; is something you gain, just after you needed it most.

When faced with two choices, simply toss a coin. It works not because it settles the question for you. But because in that brief moment while the coin is in the air. You suddenly know what you are hoping for.
Community Veteran
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Re: One for the mathematicians out there...

The mind boggles!  Cheesy
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Re: One for the mathematicians out there...

Well, the original question has me snookered, think my brain has gone to pot - I need a rest Cheesy

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Re: One for the mathematicians out there...

Give us a break Wink Wink
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Re: One for the mathematicians out there...

Quote from: Petlew
1 red will be removed at each odd numbered stroke of the cue followed by a colour on the even strokes.but this colour will be replaced on its starting spot until after all the reds are potted, after that the colours will go consecutively and not replaced.

Unless of course a 'free ball' is declared at one (or more) points in the game - which of course changes the equation a tad? Cheesy
M
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Re: One for the mathematicians out there...

Right on cue with that one MauriceC.
Experience; is something you gain, just after you needed it most.

When faced with two choices, simply toss a coin. It works not because it settles the question for you. But because in that brief moment while the coin is in the air. You suddenly know what you are hoping for.
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Re: One for the mathematicians out there...

Yep, chalk that one up.Wink
\Runs to hide behind the cushion

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Courage is resistance to fear, mastery of fear, not absence of fear - Mark Twain
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