How many balls can you place on a snooker table?

[SquaredCue]

Hello snooker enthusiasts,

This is a fun generic snooker topic for anyone, not directly SnookerQ related. The question to answer is the following:

What is the maximum number of standard snooker balls one can place on a standard snooker table so that all balls are resting on the table bed?

If you feel like thinking out loud, go ahead and post your way of calculation, however, it could be more fun if you post only the final result of your calculation first, letting other members post their number. Later on, we will discuss it and hopefully come to an agreement about the correct answer.

Please don't search the net for the answer.

The official dimensions and ball size can be found in the OFFICIAL RULES OF THE GAMES OF SNOOKER AND ENGLISH BILLIARDS.

GLHF!

[trip2hell2]

2176

[SquaredCue]

Thanks for the effort, trip2hell2!

We need some more people to join with their final result. Come on, do your math and post your numbers.

[SquaredCue]

bees.jpg (40.84 KiB) Viewed 69898 times

[edje]

976

[dan2909]

2302

[Origin]

128000

[ViPeR]

I have to be honest, this drove me nuts..... and in the end i gave up,
But i managed to balance 2 pinks on top of 2 reds.....
so my guess is 4

table.png (103.06 KiB) Viewed 69380 times

[ViPeR]

128000

was you stacking the balls like this steve

table 2.png (250.9 KiB) Viewed 69379 times

[MRaja]

lmao!

[Origin]

128000

was you stacking the balls like this steve



table 2.png

no , put reds along black cush and balls along length ways then calculated it

[SquaredCue]

... put reds along black cush and balls along length ways then calculated it

That's a pretty good strategy to start with. You must have made a mistake in the calculation, though, as the number you posted is much too large.

As you will see, this method will not yield the correct answer because you are leaving too much empty space between the balls. Bee more thorough.

[Wizard]

I think we need to refer back to the original question here before we construct the great pyramids. Pretty sure the question referred to how many you can place "on the table" not several layers above it. My question would be do you mean how many you can fit on it or how many you can place on the table within the rules? There is then the question of the purple and orange balls from days gone by ( yes I am that old). Are we talking about the full size table because this is relevant to the answer also? What a dilemma!!

[SquaredCue]

I think we need to refer back to the original question here before we construct the great pyramids. Pretty sure the question referred to how many you can place "on the table" not several layers above it.

Exactly: "all balls are resting on the table bed"

My question would be do you mean how many you can fit on it or how many you can place on the table within the rules?

The rules define the table size and the ball size. The subtle snooker rules don't apply here of course. You have hundreds of snooker ball sets to work with.

There is then the question of the purple and orange balls from days gone by ( yes I am that old). Are we talking about the full size table because this is relevant to the answer also? What a dilemma!!

Sure, it's the full size snooker table, the only standard size. And the standard snooker ball size. You can use the purple and the orange of Snooker Plus but colours don't matter, only the number of the balls you place on the cloth.

Good luck!

[ZORRO]

2592
6 balls per 1ft, so 6x12=72 length then 6x6=36 width...so 72x36=2592.

[SquaredCue]

2592

That's a good approximation but you are leaving too much empty space between the balls.

[ZORRO]

Ah so you arrange the balls staggered rather than columns, like the honeycomb, hence the picture of the bees.
That`s a bit harder to calculate.

[SquaredCue]

Yes, Zorro, that was my point with that honeycomb picture. For comparision, see how the red triangle would look like with the rows and columns method:

[Captain-Fantastic]

Hmmmm....so how can it be worked out then?...

[SquaredCue]

Hmmmm....so how can it be worked out then?...

distances.png (89.87 KiB) Viewed 64117 times

[ZORRO]

This is my last guess.....2,695.......

[SquaredCue]

This is my last guess.....2,695.......

Your previous number was a little closer.

[ZORRO]

This is my last last guess
So...I`ll halve the number that I added because of the honeycomb affect.

2,644

[Captain-Fantastic]

What`s the answer....goddamit!!!

[SquaredCue]

I'm not the best googler but I couldn't find what I beleive is the correct answer anywhere on the net! This SnookerQ forum can be the world's first place to get it right! Let's go for it step by step!

First of all, the sizes. As we are looking for the maximum number of balls, we will calculate with the largest table size and the smallest ball size the strict rules allow:

Table size: 3569 x 1778 mm (plus or minus 13 mm) => 3582 x 1791 mm
Ball diameter: 52.5 mm (plus or minus 0.05 mm) => 52.45 mm

Let's begin with columns of balls put together in honeycomb style so that the balls are always touching. Starting from the lower left corner, 34 balls will fit in the first column and every odd column. With the half ball offset applied for the 2nd and all other even columns, 33 balls will fit there as shown in this picture:

Columns of balls, honecomb style

sntmnobcols1.png (4.23 KiB) Viewed 63979 times

Somebody please help and calculate the number of columns that will fit.
How many odd columns? Let's call it Co.
How many even columns? Let's call it Ce.
So, the total number of balls that fit on the table this way is (Co * 34) + (Ce * 33) = ?