Puzzles with numbers and things

[davis_greatest]

Never tried this before... this is a test:




Edit - it seemed to work! You need to click on it to enlarge it to read it. It is the matrix requested by rambon, showing the number of ways of getting each break from 1 to 147, broken down by number of pots (1 to 36).

[rambon]

Quote:
Originally Posted by The Statman
Yes – one red, yellow, followed by five reds, yellow, five reds, green and two reds is probably the most obvious one he hasn't got to yet.

Agreed. To my disbelief, I noticed that very omission immediately upon glancing at his list. I made six 20-breaks with exactly that combination last time I played.

And I potted the yellow again afterwards for a 22 this lunchtime, but I'm sure he'll have that on his list of 22 breaks already..

Seriously, I did pot three reds in one shot last time I played - two were in the jaws of the pocket in a touching ball plant which I played at pace, went in to two more reds, one of which went in. 3 of the 4 left on the table and my mate needed snookers....

[davis_greatest]

Yes – one red, yellow, followed by five reds, yellow, five reds, green and two reds is probably the most obvious one he hasn't got to yet.

Agreed. To my disbelief, I noticed that very omission immediately upon glancing at his list. I made six 20-breaks with exactly that combination last time I played.

[The Statman]

chasmmi, I've made and seen many a 20 break, but never yet one with any of the combinations you've shown (8+ reds on the first shot). I think there are still a lot more to go before you get down to just one red...

Yes – one red, yellow, followed by five reds, yellow, five reds, green and two reds is probably the most obvious one he hasn't got to yet.

[davis_greatest]

This is the number of ways i found of making a 20 break before giving up at the enormaty of it.

15 REDS BLUE
15 REDS GREEN YELLOW

...
...
8 REDS YELLOW RED BLUE RED GREEN
8 REDS YELLOW RED BLUE RED YELLOW RED

chasmmi, I've made and seen many a 20 break, but never yet one with any of the combinations you've shown (8+ reds on the first shot). I think there are still a lot more to go before you get down to just one red...

[davis_greatest]

Don't worry about it, it was half flippant, half interested.

I will probably do it anyway - before The Statman asks me to The breakdown by number of pots makes it easier to see what is going on. I still don't know how to show it though...

[rambon]

Do you mean a matrix showing

(a) the numbers in this post:

http://www.thesnookerforum.com/showp...ount_1367.html

which shows the possibilities where the order of the pots matters (so 14 red-blacks and then red-pink is different from red-pink and then 14 red blacks)

OR

(b) the numbers in this post:

http://www.thesnookerforum.com/showp...ount_1380.html

which shows the possibilities where the order of the pots does not matter (so 14 red-blacks and then red-pink is counted as the same as red-pink and then 14 red blacks)?


If you mean (b), it's a bit tricky to calculate because again, I did not split out the calculations by number of pots. It can be done, but would take probably take at least 10 or more likely 15 minutes to calculate the breakdown. Let me know if you want it done.

Either way, getting the numbers into a matrix is not the problem. The problem is making the matrix appear on the thread in a readable format. Any ideas how to post it?

Don't worry about it, it was half flippant, half interested.

[davis_greatest]

Interesting. So this is the number of combinations of balls to make each break.

Yes, excluding in all cases, as previously pointed out, the following:

- breaks using a free ball
- breaks where more than one red is potted in a stroke
- breaks where a player comes to the table "on" a colour with reds still on the table, having been called for a "miss" on a colour on his previous shot and been put in by his opponent to play again.

[chasmmi]

I believe that is 543 and counting if you are interested.

[The Statman]

Something like this?

Break …. Number of ways
1 ……….. 1
2 ……….. 1
3 ……….. 2
4 ……….. 3
5 ……….. 5
....
146 ……. 1
147 ……. 1

Interesting. So this is the number of combinations of balls to make each break.

[chasmmi]

This is the number of ways i found of making a 20 break before giving up at the enormaty of it.

15 REDS BLUE
15 REDS GREEN YELLOW
14 REDS PINK
14 REDS BLUE RED
14 REDS BROWN YELLOW
14 REDS GREEN RED YELLOW
14 REDS YELLOW RED GREEN
13 REDS BLACK
13 REDS PINK RED
13 REDS BLUE 2 REDS
13 REDS BLUE YELLOW
13 REDS BROWN RED YELLOW
13 REDS GREEN 2 REDS YELLOW
13 REDS GREEN RED GREEN
13 REDS GREEN RED YELLOW RED
13 REDS YELLOW 2 REDS GREEN
13 REDS YELLOW RED BROWN
13 REDS YELLOW RED GREEN RED
13 REDS YELLOW RED YELLOW YELLOW
13 REDS YELLOW YELLOW GREEN
12 REDS BLACK RED
12 REDS PINK 2 REDS
12 REDS PINK YELLOW
12 REDS BLUE 3 REDS
12 REDS BLUE RED YELLOW
12 REDS BROWN 2 REDS YELLOW
12 REDS BROWN RED GREEN
12 REDS GREEN 3 REDS YELLOW
12 REDS GREEN 2 REDS GREEN
12 REDS GREEN 2 REDS YELLOW RED
12 REDS GREEN RED BROWN
12 REDS GREEN RED GREEN RED
12 REDS GREEN RED YELLOW 2 REDS
12 REDS GREEN RED YELLOW YELLOW
12 REDS GREEN YELLOW GREEN
11 REDS BLACK 2 REDS
11 REDS BLACK YELLOW
11 REDS PINK 3 REDS
11 REDS PINK RED YELLOW
11 REDS BLUE 4 REDS
11 REDS BLUE 2 REDS YELLOW
11 REDS BLUE RED GREEN
11 REDS BLUE RED YELLOW RED
11 REDS BROWN 3 REDS YELLOW
11 REDS BROWN 2 REDS GREEN
11 REDS BROWN 2 REDS YELLOW RED
11 REDS BROWN RED BROWN
11 REDS BROWN RED GREEN RED
11 REDS BROWN RED YELLOW 2 REDS
11 REDS BROWN RED YELLOW YELLOW
11 REDS BROWN YELLOW GREEN
11 REDS GREEN 4 REDS YELLOW
11 REDS GREEN 3 REDS GREEN
11 REDS GREEN 3 REDS YELLOW RED
11 REDS GREEN 2 REDS BROWN
11 REDS GREEN 2 REDS GREEN RED
11 REDS GREEN 2 REDS YELLOW 2 REDS
11 REDS GREEN 2 REDS YELLOW YELLOW
11 REDS GREEN RED BLUE
11 REDS GREEN RED BROWN RED
11 REDS GREEN RED GREEN 2 REDS
11 REDS GREEN RED GREEN YELLOW
11 REDS GREEN RED YELLOW 3 REDS
11 REDS GREEN RED YELLOW RED YELLOW
11 REDS YELLOW 4 REDS GREEN
11 REDS YELLOW 3 REDS BROWN
11 REDS YELLOW 3 REDS GREEN RED
11 REDS YELLOW 3 REDS YELLOW YELLOW
11 REDS YELLOW 2 REDS BLUE
11 REDS YELLOW 2 REDS BROWN RED
11 REDS YELLOW 2 REDS GREEN 2 REDS
11 REDS YELLOW 2 REDS GREEN YELLOW
11 REDS YELLOW 2 REDS YELLOW RED YELLOW
11 REDS YELLOW RED PINK
11 REDS YELLOW RED BLUE RED
11 REDS YELLOW RED BROWN 2 REDS
11 REDS YELLOW RED BROWN YELLOW
11 REDS YELLOW RED GREEN 3 REDS
11 REDS YELLOW RED GREEN RED YELLOW
11 REDS YELLOW RED YELLOW 2 REDS YELLOW
11 REDS YELLOW RED YELLOW RED GREEN
11 REDS YELLOW RED YELLOW RED YELLOW RED
10 REDS BLACK 3 REDS
10 REDS BLACK RED YELLOW
10 REDS PINK 4 REDS
10 REDS PINK 2 REDS YELLOW
10 REDS PINK RED GREEN
10 REDS PINK RED YELLOW RED
10 REDS BLUE 5 REDS
10 REDS BLUE 3 REDS YELLOW
10 REDS BLUE 2 REDS GREEN
10 REDS BLUE 2 REDS YELLOW RED
10 REDS BLUE RED BROWN
10 REDS BLUE RED GREEN RED
10 REDS BLUE RED YELLOW 2 REDS
10 REDS BLUE RED YELLOW YELLOW
10 REDS BLUE YELLOW GREEN
10 REDS BROWN 4 REDS YELLOW
10 REDS BROWN 3 REDS GREEN
10 REDS BROWN 3 REDS YELLOW RED
10 REDS BROWN 2 REDS BROWN
10 REDS BROWN 2 REDS GREEN RED
10 REDS BROWN 2 REDS YELLOW 2 REDS
10 REDS BROWN 2 REDS YELLOW YELLOW
10 REDS BROWN RED BLUE
10 REDS BROWN RED BROWN RED
10 REDS BROWN RED GREEN 2 REDS
10 REDS BROWN RED GREEN YELLOW
10 REDS BROWN RED YELLOW 3 REDS
10 REDS BROWN RED YELLOW RED YELLOW
10 REDS BROWN RED YELLOW GREEN
10 REDS GREEN 5 REDS YELLOW
10 REDS GREEN 4 REDS GREEN
10 REDS GREEN 4 REDS YELLOW RED
10 REDS GREEN 3 REDS BROWN
10 REDS GREEN 3 REDS GREEN RED
10 REDS GREEN 3 REDS YELLOW 2 REDS
10 REDS GREEN 3 REDS YELLOW YELLOW
10 REDS GREEN 2 REDS BLUE
10 REDS GREEN 2 REDS BROWN RED
10 REDS GREEN 2 REDS GREEN 2 REDS
10 REDS GREEN 2 REDS GREEN YELLOW
10 REDS GREEN 2 REDS YELLOW 3 REDS
10 REDS GREEN 2 REDS YELLOW RED YELLOW
10 REDS GREEN RED PINK
10 REDS GREEN RED BLUE RED
10 REDS GREEN RED BROWN 2 REDS
10 REDS GREEN RED BROWN YELLOW
10 REDS GREEN RED GREEN 3 REDS
10 REDS GREEN RED GREEN RED YELLOW
10 REDS GREEN RED YELLOW 4 REDS
10 REDS GREEN RED YELLOW 2 REDS YELLOW
10 REDS GREEN RED YELLOW RED GREEN
10 REDS GREEN RED YELLOW RED YELLOW RED
10 REDS YELLOW 5 REDS GREEN
10 REDS YELLOW 4 REDS BROWN
10 REDS YELLOW 4 REDS GREEN RED
10 REDS YELLOW 4 REDS YELLOW YELLOW
10 REDS YELLOW 3 REDS BLUE
10 REDS YELLOW 3 REDS BROWN RED
10 REDS YELLOW 3 REDS GREEN 2 REDS
10 REDS YELLOW 3 REDS GREEN YELLOW
10 REDS YELLOW 3 REDS YELLOW RED YELLOW
10 REDS YELLOW 2 REDS PINK
10 REDS YELLOW 2 REDS BLUE RED
10 REDS YELLOW 2 REDS BROWN 2 REDS
10 REDS YELLOW 2 REDS BROWN YELLOW
10 REDS YELLOW 2 REDS GREEN 3 REDS
10 REDS YELLOW 2 REDS GREEN RED YELLOW
10 REDS YELLOW 2 REDS YELLOW 2 REDS YELLOW
10 REDS YELLOW 2 REDS YELLOW RED GREEN
10 REDS YELLOW 2 REDS YELLOW RED YELLOW RED
10 REDS YELLOW RED BLACK
10 REDS YELLOW RED PINK RED
10 REDS YELLOW RED BLUE 2 REDS
10 REDS YELLOW RED BLUE YELLOW
10 REDS YELLOW RED BROWN 3 REDS
10 REDS YELLOW RED BROWN RED YELLOW
10 REDS YELLOW RED GREEN 4 REDS
10 REDS YELLOW RED GREEN 2 REDS YELLOW
10 REDS YELLOW RED GREEN RED GREEN
10 REDS YELLOW RED YELLOW 3 REDS YELLOW
10 REDS YELLOW RED YELLOW 2 REDS GREEN
10 REDS YELLOW RED YELLOW 2 REDS YELLOW RED
10 REDS YELLOW RED YELLOW RED BROWN
10 REDS YELLOW RED YELLOW RED GREEN RED
10 REDS YELLOW RED YELLOW RED YELLOW 2 REDS
10 REDS YELLOW RED YELLOW RED YELLOW YELLOW
10 REDS YELLOW RED YELLOW YELLOW GREEN
9 REDS BLACK 4 REDS
9 REDS BLACK 2 REDS YELLOW
9 REDS BLACK RED GREEN
9 REDS BLACK RED YELLOW RED
9 REDS PINK 5 REDS
9 REDS PINK 3 REDS YELLOW
9 REDS PINK 2 REDS GREEN
9 REDS PINK 2 REDS YELLOW RED
9 REDS PINK RED BROWN
9 REDS PINK RED GREEN RED
9 REDS PINK RED YELLOW 2 REDS
9 REDS PINK RED YELLOW YELLOW
9 REDS PINK YELLOW GREEN
9 REDS BLUE 6 REDS
9 REDS BLUE 4 REDS YELLOW
9 REDS BLUE 3 REDS GREEN
9 REDS BLUE 3 REDS YELLOW RED
9 REDS BLUE 2 REDS BROWN
9 REDS BLUE 2 REDS GREEN RED
9 REDS BLUE 2 REDS YELLOW 2 REDS
9 REDS BLUE 2 REDS YELLOW YELLOW
9 REDS BLUE RED BLUE
9 REDS BLUE RED BROWN RED
9 REDS BLUE RED GREEN 2 REDS
9 REDS BLUE RED GREEN YELLOW
9 REDS BLUE RED YELLOW 3 REDS
9 REDS BLUE RED YELLOW RED YELLOW
9 REDS BROWN 5 REDS YELLOW
9 REDS BROWN 4 REDS GREEN
9 REDS BROWN 4 REDS YELLOW RED
9 REDS BROWN 3 REDS BROWN
9 REDS BROWN 3 REDS GREEN RED
9 REDS BROWN 3 REDS YELLOW 2 REDS
9 REDS BROWN 3 REDS YELLOW YELLOW
9 REDS BROWN 2 REDS BLUE
9 REDS BROWN 2 REDS BROWN RED
9 REDS BROWN 2 REDS GREEN 2 REDS
9 REDS BROWN 2 REDS GREEN YELLOW
9 REDS BROWN 2 REDS YELLOW 3 REDS
9 REDS BROWN 2 REDS YELLOW RED YELLOW
9 REDS BROWN RED PINK
9 REDS BROWN RED BLUE RED
9 REDS BROWN RED BROWN 2 REDS
9 REDS BROWN RED BROWN YELLOW
9 REDS BROWN RED GREEN 3 REDS
9 REDS BROWN RED GREEN RED YELLOW
9 REDS BROWN RED YELLOW 4 REDS
9 REDS BROWN RED YELLOW 2 REDS YELLOW
9 REDS BROWN RED YELLOW RED YELLOW RED
9 REDS GREEN 6 REDS YELLOW
9 REDS GREEN 5 REDS GREEN
9 REDS GREEN 5 REDS YELLOW RED
9 REDS GREEN 4 REDS BROWN
9 REDS GREEN 4 REDS GREEN RED
9 REDS GREEN 4 REDS YELLOW 2 REDS
9 REDS GREEN 4 REDS YELLOW YELLOW
9 REDS GREEN 3 REDS BLUE
9 REDS GREEN 3 REDS BROWN RED
9 REDS GREEN 3 REDS GREEN 2 REDS
9 REDS GREEN 3 REDS GREEN YELLOW
9 REDS GREEN 3 REDS YELLOW 3 REDS
9 REDS GREEN 3 REDS YELLOW RED YELLOW
9 REDS GREEN 2 REDS PINK
9 REDS GREEN 2 REDS BLUE RED
9 REDS GREEN 2 REDS BROWN 2 REDS
9 REDS GREEN 2 REDS BROWN YELLOW
9 REDS GREEN 2 REDS GREEN 3 REDS
9 REDS GREEN 2 REDS GREEN RED YELLOW
9 REDS GREEN 2 REDS YELLOW 4 REDS
9 REDS GREEN 2 REDS YELLOW 2 REDS YELLOW
9 REDS GREEN 2 REDS YELLOW RED GREEN
9 REDS GREEN 2 REDS YELLOW RED YELLOW RED
9 REDS GREEN RED BLACK
9 REDS GREEN RED PINK RED
9 REDS GREEN RED BLUE 2 REDS
9 REDS GREEN RED BLUE YELLOW
9 REDS GREEN RED BROWN 3 REDS
9 REDS GREEN RED BROWN RED YELLOW
9 REDS GREEN RED GREEN 4 REDS
9 REDS GREEN RED GREEN 2 REDS YELLOW
9 REDS GREEN RED GREEN RED GREEN
9 REDS GREEN RED GREEN RED YELLOW RED
9 REDS GREEN RED YELLOW 5 REDS
9 REDS GREEN RED YELLOW 3 REDS YELLOW
9 REDS GREEN RED YELLOW 2 REDS GREEN
9 REDS GREEN RED YELLOW 2 REDS YELLOW RED
9 REDS GREEN RED YELLOW RED BROWN
9 REDS GREEN RED YELLOW RED GREEN RED
9 REDS GREEN RED YELLOW RED YELLOW 2 REDS
9 REDS GREEN RED YELLOW RED YELLOW YELLOW
9 REDS GREEN RED YELLOW YELLOW GREEN
9 REDS YELLOW 6 REDS GREEN
9 REDS YELLOW 5 REDS BROWN
9 REDS YELLOW 5 REDS GREEN RED
9 REDS YELLOW 5 REDS YELLOW YELLOW
9 REDS YELLOW 4 REDS BLUE
9 REDS YELLOW 4 REDS BROWN RED
9 REDS YELLOW 4 REDS GREEN 2 REDS
9 REDS YELLOW 4 REDS GREEN YELLOW
9 REDS YELLOW 4 REDS YELLOW RED YELLOW
9 REDS YELLOW 3 REDS PINK
9 REDS YELLOW 3 REDS BLUE RED
9 REDS YELLOW 3 REDS BROWN 2 REDS
9 REDS YELLOW 3 REDS BROWN YELLOW
9 REDS YELLOW 3 REDS GREEN 3 REDS
9 REDS YELLOW 3 REDS GREEN RED YELLOW
9 REDS YELLOW 3 REDS YELLOW 2 REDS YELLOW
9 REDS YELLOW 3 REDS YELLOW RED GREEN
9 REDS YELLOW 3 REDS YELLOW RED YELLOW RED
9 REDS YELLOW 2 REDS BLACK
9 REDS YELLOW 2 REDS PINK RED
9 REDS YELLOW 2 REDS BLUE 2 REDS
9 REDS YELLOW 2 REDS BLUE YELLOW
9 REDS YELLOW 2 REDS BROWN 3 REDS
9 REDS YELLOW 2 REDS BROWN RED YELLOW
9 REDS YELLOW 2 REDS GREEN 4 REDS
9 REDS YELLOW 2 REDS GREEN 2 REDS YELLOW
9 REDS YELLOW 2 REDS GREEN RED GREEN
9 REDS YELLOW 2 REDS GREEN RED YELLOW RED
9 REDS YELLOW 2 REDS YELLOW 3 REDS YELLOW
9 REDS YELLOW 2 REDS YELLOW 2 REDS GREEN
9 REDS YELLOW 2 REDS YELLOW 2 REDS YELLOW RED
9 REDS YELLOW 2 REDS YELLOW RED BROWN
9 REDS YELLOW 2 REDS YELLOW RED GREEN RED
9 REDS YELLOW 2 REDS YELLOW RED YELLOW 2 REDS
9 REDS YELLOW 2 REDS YELLOW RED YELLOW YELLOW
9 REDS YELLOW 2 REDS YELLOW YELLOW GREEN
9 REDS YELLOW RED BLACK RED
9 REDS YELLOW RED PINK 2 REDS
9 REDS YELLOW RED PINK YELLOW
9 REDS YELLOW RED BLUE 3 REDS
9 REDS YELLOW RED BLUE RED YELLOW
9 REDS YELLOW RED BROWN 4 REDS
9 REDS YELLOW RED BROWN 2 REDS YELLOW
9 REDS YELLOW RED BROWN RED GREEN
9 REDS YELLOW RED BROWN RED YELLOW RED
9 REDS YELLOW RED GREEN 5 REDS
9 REDS YELLOW RED GREEN 3 REDS YELLOW
9 REDS YELLOW RED GREEN 2 REDS GREEN
9 REDS YELLOW RED GREEN 2 REDS YELLOW RED
9 REDS YELLOW RED GREEN RED BROWN
9 REDS YELLOW RED GREEN RED GREEN RED
9 REDS YELLOW RED GREEN RED YELLOW 2 REDS
9 REDS YELLOW RED GREEN RED YELLOW YELLOW
9 REDS YELLOW RED GREEN YELLOW GREEN
9 REDS YELLOW RED YELLOW 4 REDS YELLOW
9 REDS YELLOW RED YELLOW 3 REDS GREEN
9 REDS YELLOW RED YELLOW 3 REDS YELLOW RED
9 REDS YELLOW RED YELLOW 2 REDS BROWN
9 REDS YELLOW RED YELLOW 2 REDS GREEN RED
9 REDS YELLOW RED YELLOW 2 REDS YELLOW 2 REDS
9 REDS YELLOW RED YELLOW 2 REDS YELLOW YELLOW
9 REDS YELLOW RED YELLOW RED BLUE
9 REDS YELLOW RED YELLOW RED BROWN RED
9 REDS YELLOW RED YELLOW RED GREEN 2 REDS
9 REDS YELLOW RED YELLOW RED GREEN YELLOW
9 REDS YELLOW RED YELLOW RED YELLOW 3 REDS
9 REDS YELLOW RED YELLOW RED YELLOW RED YELLOW
9 REDS YELLOW YELLOW GREEN BROWN
8 REDS BLACK 5 REDS
8 REDS BLACK 3 REDS YELLOW
8 REDS BLACK 2 REDS GREEN
8 REDS BLACK 2 REDS YELLOW RED
8 REDS BLACK RED BROWN
8 REDS BLACK RED GREEN RED
8 REDS BLACK RED YELLOW 2 REDS
8 REDS BLACK RED YELLOW YELLOW
8 REDS BLACK YELLOW GREEN
8 REDS PINK 6 REDS
8 REDS PINK 4 REDS YELLOW
8 REDS PINK 3 REDS GREEN
8 REDS PINK 3 REDS YELLOW RED
8 REDS PINK 2 REDS BROWN
8 REDS PINK 2 REDS GREEN RED
8 REDS PINK 2 REDS YELLOW 2 REDS
8 REDS PINK 2 REDS YELLOW YELLOW
8 REDS PINK RED BLUE
8 REDS PINK RED BROWN RED
8 REDS PINK RED GREEN 2 REDS
8 REDS PINK RED GREEN YELLOW
8 REDS PINK RED YELLOW 3 REDS
8 REDS PINK RED YELLOW RED YELLOW
8 REDS BLUE 7 REDS
8 REDS BLUE 5 REDS YELLOW
8 REDS BLUE 4 REDS GREEN
8 REDS BLUE 4 REDS YELLOW RED
8 REDS BLUE 3 REDS BROWN
8 REDS BLUE 3 REDS GREEN RED
8 REDS BLUE 3 REDS YELLOW 2 REDS
8 REDS BLUE 3 REDS YELLOW YELLOW
8 REDS BLUE 2 REDS BLUE
8 REDS BLUE 2 REDS BROWN RED
8 REDS BLUE 2 REDS GREEN 2 REDS
8 REDS BLUE 2 REDS GREEN YELLOW
8 REDS BLUE 2 REDS YELLOW 3 REDS
8 REDS BLUE 2 REDS YELLOW RED YELLOW
8 REDS BLUE RED PINK
8 REDS BLUE RED BLUE RED
8 REDS BLUE RED BROWN 2 REDS
8 REDS BLUE RED BROWN YELLOW
8 REDS BLUE RED GREEN 3 REDS
8 REDS BLUE RED GREEN RED YELLOW
8 REDS BLUE RED YELLOW 4 REDS
8 REDS BLUE RED YELLOW 2 REDS YELLOW
8 REDS BLUE RED YELLOW RED GREEN
8 REDS BLUE RED YELLOW RED YELLOW RED
8 REDS BROWN 6 REDS YELLOW
8 REDS BROWN 5 REDS GREEN
8 REDS BROWN 5 REDS YELLOW RED
8 REDS BROWN 4 REDS BROWN
8 REDS BROWN 4 REDS GREEN RED
8 REDS BROWN 4 REDS YELLOW 2 REDS
8 REDS BROWN 4 REDS YELLOW YELLOW
8 REDS BROWN 3 REDS BLUE
8 REDS BROWN 3 REDS BROWN RED
8 REDS BROWN 3 REDS GREEN 2 REDS
8 REDS BROWN 3 REDS GREEN YELLOW
8 REDS BROWN 2 REDS PINK
8 REDS BROWN 2 REDS BLUE RED
8 REDS BROWN 2 REDS BROWN 2 REDS
8 REDS BROWN 2 REDS BROWN YELLOW
8 REDS BROWN 2 REDS GREEN 3 REDS
8 REDS BROWN 2 REDS GREEN RED YELLOW
8 REDS BROWN 2 REDS YELLOW 4 REDS
8 REDS BROWN 2 REDS YELLOW 2 REDS YELLOW
8 REDS BROWN 2 REDS YELLOW RED GREEN
8 REDS BROWN 2 REDS YELLOW RED YELLOW RED
8 REDS BROWN RED BLACK
8 REDS BROWN RED PINK RED
8 REDS BROWN RED BLUE 2 REDS
8 REDS BROWN RED BLUE YELLOW
8 REDS BROWN RED BROWN 3 REDS
8 REDS BROWN RED BROWN RED YELLOW
8 REDS BROWN RED GREEN 4 REDS
8 REDS BROWN RED GREEN 2 REDS YELLOW
8 REDS BROWN RED GREEN RED GREEN
8 REDS BROWN RED GREEN RED YELLOW RED
8 REDS BROWN RED YELLOW 5 REDS
8 REDS BROWN RED YELLOW 3 REDS YELLOW
8 REDS BROWN RED YELLOW 2 REDS GREEN
8 REDS BROWN RED YELLOW 2 REDS YELLOW RED
8 REDS BROWN RED YELLOW RED BROWN
8 REDS BROWN RED YELLOW RED GREEN RED
8 REDS BROWN RED YELLOW RED YELLOW 2 REDS
8 REDS BROWN RED YELLOW RED YELLOW YELLOW
8 REDS BROWN RED YELLOW YELLOW GREEN
8 REDS GREEN 7 REDS YELLOW
8 REDS GREEN 6 REDS GREEN
8 REDS GREEN 6 REDS YELLOW RED
8 REDS GREEN 5 REDS BROWN
8 REDS GREEN 5 REDS GREEN RED
8 REDS GREEN 5 REDS YELLOW 2 REDS
8 REDS GREEN 5 REDS YELLOW YELLOW
8 REDS GREEN 4 REDS BLUE
8 REDS GREEN 4 REDS BROWN RED
8 REDS GREEN 4 REDS GREEN 2 REDS
8 REDS GREEN 4 REDS GREEN YELLOW
8 REDS GREEN 4 REDS YELLOW 3 REDS
8 REDS GREEN 4 REDS YELLOW RED YELLOW
8 REDS GREEN 3 REDS PINK
8 REDS GREEN 3 REDS BLUE RED
8 REDS GREEN 3 REDS BROWN 2 REDS
8 REDS GREEN 3 REDS BROWN YELLOW
8 REDS GREEN 3 REDS GREEN 3 REDS
8 REDS GREEN 3 REDS GREEN RED YELLOW
8 REDS GREEN 3 REDS YELLOW 4 REDS
8 REDS GREEN 3 REDS YELLOW 2 REDS YELLOW
8 REDS GREEN 3 REDS YELLOW RED GREEN
8 REDS GREEN 3 REDS YELLOW RED YELLOW RED
8 REDS GREEN 2 REDS BLACK
8 REDS GREEN 2 REDS PINK RED
8 REDS GREEN 2 REDS BLUE 2 REDS
8 REDS GREEN 2 REDS BLUE YELLOW
8 REDS GREEN 2 REDS BROWN 3 REDS
8 REDS GREEN 2 REDS BROWN RED YELLOW
8 REDS GREEN 2 REDS GREEN 4 REDS
8 REDS GREEN 2 REDS GREEN 2 REDS YELLOW
8 REDS GREEN 2 REDS GREEN RED GREEN
8 REDS GREEN 2 REDS GREEN RED YELLOW RED
8 REDS GREEN 2 REDS YELLOW 5 REDS
8 REDS GREEN 2 REDS YELLOW 3 REDS YELLOW
8 REDS GREEN 2 REDS YELLOW 2 REDS GREEN
8 REDS GREEN 2 REDS YELLOW 2 REDS YELLOW RED
8 REDS GREEN 2 REDS YELLOW RED BROWN
8 REDS GREEN 2 REDS YELLOW RED GREEN RED
8 REDS GREEN 2 REDS YELLOW RED YELLOW 2 REDS
8 REDS GREEN 2 REDS YELLOW RED YELLOW YELLOW
8 REDS GREEN 2 REDS YELLOW YELLOW GREEN
8 REDS GREEN RED BLACK RED
8 REDS GREEN RED PINK 2 REDS
8 REDS GREEN RED PINK YELLOW
8 REDS GREEN RED BLUE 3 REDS
8 REDS GREEN RED BLUE RED YELLOW
8 REDS GREEN RED BROWN 4 REDS
8 REDS GREEN RED BROWN 2 REDS YELLOW
8 REDS GREEN RED BROWN RED GREEN
8 REDS GREEN RED BROWN RED YELLOW RED
8 REDS GREEN RED GREEN 5 REDS
8 REDS GREEN RED GREEN 3 REDS YELLOW
8 REDS GREEN RED GREEN 2 REDS GREEN
8 REDS GREEN RED GREEN 2 REDS YELLOW RED
8 REDS GREEN RED GREEN RED BROWN
8 REDS GREEN RED GREEN RED GREEN RED
8 REDS GREEN RED GREEN RED YELLOW 2 REDS
8 REDS GREEN RED GREEN RED YELLOW YELLOW
8 REDS GREEN RED GREEN YELLOW GREEN
8 REDS GREEN YELLOW GREEN BROWN
8 REDS YELLOW 7 REDS GREEN
8 REDS YELLOW 7 REDS YELLOW RED
8 REDS YELLOW 6 REDS BROWN
8 REDS YELLOW 6 REDS GREEN RED
8 REDS YELLOW 6 REDS YELLOW 2 REDS
8 REDS YELLOW 6 REDS YELLOW YELLOW
8 REDS YELLOW 5 REDS BLUE
8 REDS YELLOW 5 REDS BROWN RED
8 REDS YELLOW 5 REDS GREEN 2 REDS
8 REDS YELLOW 5 REDS GREEN YELLOW
8 REDS YELLOW 5 REDS YELLOW 3 REDS
8 REDS YELLOW 5 REDS YELLOW RED YELLOW
8 REDS YELLOW 4 REDS PINK
8 REDS YELLOW 4 REDS BLUE RED
8 REDS YELLOW 4 REDS BROWN 2 REDS
8 REDS YELLOW 4 REDS BROWN YELLOW
8 REDS YELLOW 4 REDS GREEN 3 REDS
8 REDS YELLOW 4 REDS GREEN RED YELLOW
8 REDS YELLOW 4 REDS YELLOW 2 REDS YELLOW
8 REDS YELLOW 4 REDS YELLOW RED GREEN
8 REDS YELLOW 4 REDS YELLOW RED YELLOW RED
8 REDS YELLOW 3 REDS BLACK
8 REDS YELLOW 3 REDS PINK RED
8 REDS YELLOW 3 REDS BLUE 2 REDS
8 REDS YELLOW 3 REDS BLUE YELLOW
8 REDS YELLOW 3 REDS BROWN 3 REDS
8 REDS YELLOW 3 REDS BROWN RED YELLOW
8 REDS YELLOW 3 REDS GREEN 4 REDS
8 REDS YELLOW 3 REDS GREEN 2 REDS YELLOW
8 REDS YELLOW 3 REDS GREEN RED GREEN
8 REDS YELLOW 3 REDS GREEN RED YELLOW RED
8 REDS YELLOW 3 REDS YELLOW 3 REDS YELLOW
8 REDS YELLOW 3 REDS YELLOW 2 REDS GREEN
8 REDS YELLOW 3 REDS YELLOW 2 REDS YELLOW RED
8 REDS YELLOW 3 REDS YELLOW RED BROWN
8 REDS YELLOW 3 REDS YELLOW RED GREEN RED
8 REDS YELLOW 3 REDS YELLOW RED YELLOW 2 REDS
8 REDS YELLOW 3 REDS YELOW RED YELLOW YELLOW
8 REDS YELLOW 2 REDS BLACK RED
8 REDS YELLOW 2 REDS PINK 2 REDS
8 REDS YELLOW 2 REDS PINK YELLOW
8 REDS YELLOW 2 REDS BLUE 3 REDS
8 REDS YELLOW 2 REDS BLUE RED YELLOW
8 REDS YELLOW 2 REDS BROWN 4 REDS
8 REDS YELLOW 2 REDS BROWN 2 REDS YELLOW
8 REDS YELLOW 2 REDS BROWN RED GREEN
8 REDS YELLOW 2 REDS BROWN RED YELLOW RED
8 REDS YELLOW 2 REDS GREEN 5 REDS
8 REDS YELLOW 2 REDS GREEN 3 REDS YELLOW
8 REDS YELLOW 2 REDS GREEN 2 REDS GREEN
8 REDS YELLOW 2 REDS GREEN 2 REDS YELLOW RED
8 REDS YELLOW 2 REDS GREEN RED BROWN
8 REDS YELLOW 2 REDS GREEN RED GREEN RED
8 REDS YELLOW 2 REDS GREEN RED YELLOW 2 REDS
8 REDS YELLOW 2 REDS GREEN RED YELLOW YELLOW
8 REDS YELLOW 2 REDS GREEN YELLOW GREEN
8 REDS YELLOW RED BLACK 2 REDS
8 REDS YELLOW RED BLACK YELLOW
8 REDS YELLOW RED PINK 3 REDS
8 REDS YELLOW RED PINK RED YELLOW
8 REDS YELLOW RED BLUE 4 REDS
8 REDS YELLOW RED BLUE 2 REDS YELLOW
8 REDS YELLOW RED BLUE RED GREEN
8 REDS YELLOW RED BLUE RED YELLOW RED

[davis_greatest]

How about a matrix with break total down the left, number of pots across the top and then a frequency for each in the main body....?

It would be interesting to see how that looked, but it may be too much I don't know

Do you mean a matrix showing

(a) the numbers in this post:

http://www.thesnookerforum.com/showp...ount_1367.html

which shows the possibilities where the order of the pots matters (so 14 red-blacks and then red-pink is different from red-pink and then 14 red blacks)

OR

(b) the numbers in this post:

http://www.thesnookerforum.com/showp...ount_1380.html

which shows the possibilities where the order of the pots does not matter (so 14 red-blacks and then red-pink is counted as the same as red-pink and then 14 red blacks)?


If you mean (b), it's a bit tricky to calculate because again, I did not split out the calculations by number of pots. It can be done, but would take probably take at least 10 or more likely 15 minutes to calculate the breakdown. Let me know if you want it done.

Either way, getting the numbers into a matrix is not the problem. The problem is making the matrix appear on the thread in a readable format. Any ideas how to post it?

[dantuck_7]

Yep that would be good.

[rambon]

How about a matrix with break total down the left, number of pots across the top and then a frequency for each in the main body....?

It would be interesting to see how that looked, but it may be too much I don't know

[davis_greatest]

Thank you. That is indeed interesting. Maybe we (you) could simplify the number of ways eliminating the cases where one set of colours-after-reds is an 'anagram' of another, by which I mean, for example a 146 can be made in only 1 way – 14 reds and a pink – and the 145 can be made in only two ways – 13 reds and 2 pinks or 14 reds and a blue. In fact I will work on this myself.

Something like this?

Break …. Number of ways
1 ……….. 1
2 ……….. 1
3 ……….. 2
4 ……….. 3
5 ……….. 5
6 ……….. 5
7 ……….. 7
8 ……….. 8
9 ……….. 11
10 …….. 11
11 …….. 15
12 …….. 20
13 …….. 24
14 …….. 28
15 …….. 34
16 …….. 40
17 …….. 49
18 …….. 58
19 …….. 66
20 …….. 81
21 …….. 93
22 …….. 107
23 …….. 124
24 …….. 144
25 …….. 166
26 …….. 189
27 …….. 215
28 …….. 245
29 …….. 279
30 …….. 314
31 …….. 352
32 …….. 400
33 …….. 448
34 …….. 498
35 …….. 558
36 …….. 622
37 …….. 690
38 …….. 766
39 …….. 846
40 …….. 936
41 …….. 1034
42 …….. 1135
43 …….. 1245
44 …….. 1371
45 …….. 1500
46 …….. 1635
47 …….. 1788
48 …….. 1949
49 …….. 2118
50 …….. 2300
51 …….. 2491
52 …….. 2695
53 …….. 2912
54 …….. 3135
55 …….. 3370
56 …….. 3621
57 …….. 3876
58 …….. 4136
59 …….. 4412
60 …….. 4693
61 …….. 4976
62 …….. 5266
63 …….. 5556
64 …….. 5848
65 …….. 6142
66 …….. 6425
67 …….. 6706
68 …….. 6985
69 …….. 7250
70 …….. 7499
71 …….. 7740
72 …….. 7965
73 …….. 8169
74 …….. 8355
75 …….. 8520
76 …….. 8661
77 …….. 8781
78 …….. 8871
79 …….. 8937
80 …….. 8981
81 …….. 8993
82 …….. 8978
83 …….. 8940
84 …….. 8876
85 …….. 8783
86 …….. 8669
87 …….. 8530
88 …….. 8369
89 …….. 8190
90 …….. 7989
91 …….. 7770
92 …….. 7540
93 …….. 7292
94 …….. 7032
95 …….. 6764
96 …….. 6488
97 …….. 6204
98 …….. 5916
99 …….. 5625
100 ……. 5333
101 ……. 5041
102 ……. 4751
103 ……. 4463
104 ……. 4183
105 ……. 3905
106 ……. 3633
107 ……. 3371
108 ……. 3117
109 ……. 2871
110 ……. 2637
111 ……. 2412
112 ……. 2198
113 ……. 1995
114 ……. 1804
115 ……. 1624
116 ……. 1456
117 ……. 1300
118 ……. 1154
119 ……. 1021
120 ……. 897
121 ……. 785
122 ……. 683
123 ……. 591
124 ……. 508
125 ……. 435
126 ……. 369
127 ……. 311
128 ……. 260
129 ……. 217
130 ……. 178
131 ……. 146
132 ……. 118
133 ……. 94
134 ……. 75
135 ……. 59
136 ……. 45
137 ……. 35
138 ……. 26
139 ……. 20
140 ……. 14
141 ……. 10
142 ……. 7
143 ……. 5
144 ……. 3
145 ……. 2
146 ……. 1
147 ……. 1