Guy Manges
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Question is , If we take 10 pool balls and drop them on an 9' pool table, How many ball configuration can be made , Quadrillion ?
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- Thread starter Guy Manges
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Pretty sure we had this asked before and there was some math stuff happening to try to get a proper scientific answer. I think the final result was "A lot".
I think it's more than that. 5800 square inches on that table so probably 800 possible spots for each of the 10 balls? I think that's 800!/790!, Which is a massive number like 1e29. And then maybe multiply that by 10! To account for ball order.
Considering you can fit 968 balls on a 50”x100” playing surface….
That’s if they all only had close to an exact 2.25” spot to sit.
Now you have 10 balls that have the room not being taken by about 958 balls.
And, just moving them .25” or less would constitute a “different” position.
“A lot” would be a huge understatement.
That’s if they all only had close to an exact 2.25” spot to sit.
Now you have 10 balls that have the room not being taken by about 958 balls.
And, just moving them .25” or less would constitute a “different” position.
“A lot” would be a huge understatement.
That’s only if you moved a ball a complete 2.25” one way or another to be considered a different position.
Moving it just 0.25” or maybe even less would technically be a different position of a ball.
xX-Wizard-Xx
Well-known member
100,000,000,000
Easy
Surface area of pool table is 50x100= 5,000 square inches
A 2.25 inch diameter ball takes up 3.976 inches of surface area at it's circumference...
Take 5,000 inches divided by the surface area of a ball....that's 1,258. That's how many balls that could fit on a 9 foot table.
To figure all the possible combinations you need to do a mathematical calculation credit a Permutation Without Repetition.
The formula would be 1,258 times the next 9 descending whole numbers for each less spot on the table taken by the next ball....so
1,258 x 1,257 x 1,256, x 1,255 x 1,254 x 1,253 x 1,252 x 1,251 x 1,250 x 1,249 equals
9,577,054,998,202,898,152,157,349,600,000
That's 9.577 quintillion
Or 9.577 million trillions
It's a shit ton, but there's the math.
Correct, my 800 possible spots is a low estimate I made up. Let's assume it's 4x too low, my equation becomes (3200!/3190!) Multiplied by 10! , Which is some insane number like 1e35.
I don't remember if the 10! Is necessary or not for ball order, but I think the permutation equation is correct (n!/(n-r)!)
The 6 people in the world who are both pool nerds, math nerds, and happen to be bored AZB members.
There was similar math done with a deck of cards, how many times would you need to shuffle a deck to come up with two identical shuffles.
The answer was such a large number that it was basically impossible to imagine or grasp by the human brain.
Video done visually with analogies to try to sort it out. Not sure what is greater chance two same decks shuffled or two pool table layouts identical.
The answer was such a large number that it was basically impossible to imagine or grasp by the human brain.
Video done visually with analogies to try to sort it out. Not sure what is greater chance two same decks shuffled or two pool table layouts identical.
Just for curiosity sake, wouldn’t it be more than 1258?
For example, pretend the pockets are corners and not pockets. You place the cue ball tight to a corner. Now move it a microscopic distance from the side rail, but still on the short rail. Then continue that microscopic movement all the way down the rail until you touch the other side.
Those are all different positions that ball could land in and be touching the rail.
Now you have to move it away from the short/end rail a microscopic distance. And then start working backwards.
Wouldn’t that equate to a ridiculously high number that’s not just as simple as 1258 positions?
Good enough for me!
And, as a sometimes physics and precision nerd, how far can a ball move and still be considered in the same position? The plank length? What about quantum effects?
The internet is the father of largely pointless debates and questions. I mean really what is anything we do past eating and keeping our bodies alive any more important on a larger scale than anything else? Is fishing more important that picking out a right shade of blue for a shirt? Is time spend picking a TV show worth more than deciding on what beer to buy? Is ranking girls/guys at the bar that walk by over a debate who is the best cartoon character ever? I mean I bet that 95% of all things we do in life are basically pointless. Including playing pool. Humans, like all other life, has two and really only two main goals, to fuck and to try to keep alive. Everything else we build around that is fluff or something to help us do one of those two better.
Ya. You’d have to set up some parameters for the question.
But, I’d say we are high enough to call it infinite for our purposes.
As in, the odds of seeing an exact copy in one’s lifetime are basically zero. So for practical purposes, that makes the answer infinite.
It's one of my favorite things about pool. I love chess also, but chess openings are always the same and largely played from memory, so many games can be repetitive at my low skill level. Ever rack of 9 ball seems different to me.