Billiard Balls Problem
Playing pool the other day... discussion came up about how many billiard balls you could fit on a table without stacking them up.
A few points:
Regulation table measures 100"x50" inside of cushions.
Ball size 2.25" diameter
Ignore pockets
All balls must contact playing surface
No compressing the cushions!
A few points:
Regulation table measures 100"x50" inside of cushions.
Ball size 2.25" diameter
Ignore pockets
All balls must contact playing surface
No compressing the cushions!
Comments
Mathematically, your guess would incorrect!
1075, 1080 & 1081 are all incorrect... but I'm curious as to how you got to 1075.
damn. I used a cad program to map out two rows of balls to scale, and then measured the staggered balls which averaged out to 1.97" per row. in a 100" stretch you can fit 50 rows of balls, so 25 rows of 21 and 25 rows of 22. I see my mistake now though - I didn't properly take advantage of the unused 1.54" strip of dead space at the bottom, gotta be able to fit a few more in there.
Really nice... but rounding errors are not going to go unpunished... lol
In this configuration the rows of billiard balls will take up 2.25 + (n-1)*2.25*sin60° inches where n is the number of rows.
51 rows will take up 99.67785793 inches so 51 rows will fit... 26*22 + 25*21 = 1097
So you were very close... but.... 1097 isn't correct either!!
>:D
I'm going to respond to all guesses by saying they are incorrect. If you have a solution for 1099, I'd be interested in seeing it, but I suspect its a guess based on the last few posts.
No!... lol
Or I will allow it as long all billiard balls are placed to maximize the contact area between the ball and playing surface... hee hee
ship it.
how many 2.25 pool balls fit on a 9 ft 50 x 100 billiard table? [Archive] - AzBilliards.com
Never did get my $100
A quick calculation yields 10692 balls, which would weigh about 3800 lbs. If anyone wants to try this... please take a picture!! A cheap set of balls can be had for $34.99... less for bulk orders!! ... should be able to do this for about $20,000 including table.... lol
You want to know how many strap-ons fit on a pool table????
Skipping this question!
Don't worry it was kinda an inside joke re Insane Guy!;)
Pretty sure I remember that thread!
And you would be incorrect . . . :-X
1012 was done in my head quickly based on 44 balls fitting into the 100" and 22 fitting into the 50" width. Staggering the rows to allow for a row of 44 followed by a row of 43, etc.
Anyway, here is a solution for you . . .
1097
Several ways to do it:
If you start on the long cushion you can fit 44 balls (100/2.25=44.4), the next row up fits in between the balls from the first row (like in the rack - hexagonal close packing), BUT 44 balls cannot fit across (44.5*2.25=100.125), so you can only fit 43. The distance between rows is 1.94 (sin 60*2.25), and thus 25 rows. 13*44 + 12*43 = 1088.
If you start on the short rail, you can fit 22 balls in the first row but again only 21 in the row above. 51 rows will fit - 26*22 + 25*21 = 1097.
If you pack them in a standard cubic array you'd have 968.
Happy now? Besides, even if they HAD been WAG's, those were not specifically proscribed by your question.