Puzzles with numbers and things

[davis_greatest]

So here is the latest Puzzles with numbers and things Hall of Fame

Oliver (my pet orang-utan)
Gordon (my pet gorilla)
Charlie (my pet chimpanzee)
snookersfun
abextra
davis_greatest (Oliver's, Gordon's and Charlie's pet something)
Vidas
chasmmi
elvaago
robert602
Sarmu
The Statman
austrian_girl
austrian_girl's dad
Semih_Sayginer
Snooker Rocks!
Ginger_Freak
April Madness
steveb72
rambon
Microsoft Excel

[davis_greatest]

Good job, guys, very impressive!

BTW, don't you think Excel has deserved a place in the Hall of Fame?

A good idea, abetra... I'll update it now then!

[abextra]

Good job, guys, very impressive!

BTW, don't you think Excel has deserved a place in the Hall of Fame?

[snookersfun]

I graphed some of the number salad of http://www.thesnookerforum.com/showp...ount_1367.html
chemists like graphs!
so, here is the piece of art:

[The Statman]

My colourblindness? Or rambon's?

Your approach will work, but will give quite a lot of possibilities if you were planning on doing them by hand - especially when you get to 15 reds (as I think snookersfun found when she tried to list them all for a 120 total clearance ).

Let me know how you get on - I can stick a formula into Excel which should throw out all the possibilities for each break if you prefer.

Needless to say, I prefer that!

Yes, whoever's colourblindness it is, it is contagious!

[davis_greatest]

Yes that is what I meant - your colourblindness is contagious!

I guess a simple list would not be all that time-consuming; i.e. all the possibilities for one red (each of six colours after), then two reds, three reds etc. through to 15 reds. Then add 1 to each of them as another possibility (excluding 15 reds) and 2 throught 27 to each of them, as possibilities for colour clearances at the end.

My colourblindness? Or rambon's?

Your approach will work, but will give quite a lot of possibilities if you were planning on doing them by hand - especially when you get to 15 reds (as I think snookersfun found when she tried to list them all for a 120 total clearance ).

Let me know how you get on - I can stick a formula into Excel which should throw out all the possibilities for each break if you prefer.

[The Statman]

I assume you mean blacks rather than reds, where highlighted...

Do you have an idea for a straightforward way of calculating this?

Yes that is what I meant - your colourblindness is contagious!

I guess a simple list would not be all that time-consuming; i.e. all the possibilities for one red (each of six colours after), then two reds, three reds etc. through to 15 reds. Then add 1 to each of them as another possibility (excluding 15 reds) and 2 throught 27 to each of them, as possibilities for colour clearances at the end.

[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.

I assume you mean blacks rather than reds, where highlighted...

Do you have an idea for a straightforward way of calculating this?

[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.

I'm sure that can be done. Here is the answer for total clearances only (not sure whether you've already seen this?):

http://www.thesnookerforum.com/showp...ount_1345.html

[The Statman]

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.

[davis_greatest]

The Statman, I just noticed something that might interest you. Usually, if a given break is possible for two different numbers of pots (e.g. 7 pots or 9 pots), then it is also possible for the number of pots in between (e.g. 8 pots). However, there are a few cases where this does not apply. For example, breaks of 11 and 13 can each be made with 2 or 4 pots, but not with 3 pots. A break of 22 can be made with 4 or 6 pots, but not with 5 pots. A break of 25 can be made with 5 or 7 pots, but not with 6 pots.

Anyway, I'm not sure that this thread is necessarily the right place for these observations, but never mind...

[davis_greatest]

Could you break this down by number of pots?

e.g.:

Break of 1: 1 way, 1 pot
Break of 2: 1 way, 2 pots
Break of 3: 2 ways, 1× 1 pot and 1× 2pots
Break of 4: 3 ways, 1× 1 pot, 1× 2 pots and 1× 3 pots
Break of 5: 5 ways, 1× 1 pot, 2× 2 pots, 2× 3 pots
...
Break of 147: 1 way, 36 pots.

Presumably the break that can be made using the most different numbers of shots would be 72.

A break of 72 can only be made using 19 different numbers of pots (anything from 18 to 36 pots).

The most is breaks of 50 or 51 - they can be made using 21 different numbers of pots (anything from 12 to 32 pots). Fancy not knowing that!

[davis_greatest]

Sorry Statman - this isn't very pretty!

Break
1 ……..……….. 1 way: 1 x 1 pot,
2 ……..……….. 1 way: 1 x 1 pot,
3 ……..……….. 2 ways: 1 x 1 pot, 1 x 2 pots,
4 ……..……….. 3 ways: 1 x 1 pot, 1 x 2 pots, 1 x 3 pots,
5 ……..……….. 5 ways: 1 x 1 pot, 2 x 2 pots, 2 x 3 pots,
6 ……..……….. 5 ways: 1 x 1 pot, 1 x 2 pots, 2 x 3 pots, 1 x 4 pots,
7 ……..……….. 8 ways: 1 x 1 pot, 2 x 2 pots, 2 x 3 pots, 2 x 4 pots, 1 x 5 pots,
8 ……..……….. 10 ways: 1 x 2 pots, 2 x 3 pots, 4 x 4 pots, 3 x 5 pots,
9 ……..……….. 15 ways: 1 x 2 pots, 3 x 3 pots, 5 x 4 pots, 5 x 5 pots, 1 x 6 pots,
10 …………….. 18 ways: 1 x 3 pots, 6 x 4 pots, 7 x 5 pots, 3 x 6 pots, 1 x 7 pots,
11 …………….. 28 ways: 1 x 2 pots, 7 x 4 pots, 9 x 5 pots, 7 x 6 pots, 4 x 7 pots,
12 …………….. 41 ways: 1 x 3 pots, 6 x 4 pots, 12 x 5 pots, 12 x 6 pots, 9 x 7 pots, 1 x 8 pots,
13 …………….. 57 ways: 1 x 2 pots, 5 x 4 pots, 12 x 5 pots, 18 x 6 pots, 16 x 7 pots, 4 x 8 pots, 1 x 9 pots,
14 …………….. 80 ways: 4 x 4 pots, 10 x 5 pots, 25 x 6 pots, 25 x 7 pots, 11 x 8 pots, 5 x 9 pots,
15 …………….. 116 ways: 1 x 3 pots, 2 x 4 pots, 8 x 5 pots, 30 x 6 pots, 37 x 7 pots, 23 x 8 pots, 14 x 9 pots, 1 x 10 pots,
16 …………….. 165 ways: 1 x 4 pots, 6 x 5 pots, 33 x 6 pots, 48 x 7 pots, 41 x 8 pots, 30 x 9 pots, 5 x 10 pots, 1 x 11 pots,
17 …………….. 235 ways: 4 x 5 pots, 33 x 6 pots, 55 x 7 pots, 66 x 8 pots, 55 x 9 pots, 16 x 10 pots, 6 x 11 pots,
18 …………….. 338 ways: 1 x 3 pots, 1 x 4 pots, 1 x 5 pots, 30 x 6 pots, 58 x 7 pots, 95 x 8 pots, 92 x 9 pots, 39 x 10 pots, 20 x 11 pots, 1 x 12 pots,
19 …………….. 483 ways: 25 x 6 pots, 57 x 7 pots, 125 x 8 pots, 139 x 9 pots, 80 x 10 pots, 50 x 11 pots, 6 x 12 pots, 1 x 13 pots,
20 …………….. 692 ways: 1 x 5 pots, 18 x 6 pots, 52 x 7 pots, 151 x 8 pots, 190 x 9 pots, 146 x 10 pots, 105 x 11 pots, 22 x 12 pots, 7 x 13 pots,
21 …………….. 987 ways: 12 x 6 pots, 41 x 7 pots, 169 x 8 pots, 239 x 9 pots, 240 x 10 pots, 197 x 11 pots, 61 x 12 pots, 27 x 13 pots, 1 x 14 pots,
22 …………….. 1415 ways: 1 x 4 pots, 7 x 6 pots, 29 x 7 pots, 176 x 8 pots, 280 x 9 pots, 361 x 10 pots, 335 x 11 pots, 141 x 12 pots, 77 x 13 pots, 7 x 14 pots, 1 x 15 pots,
23 …………….. 2026 ways: 3 x 6 pots, 20 x 7 pots, 169 x 8 pots, 307 x 9 pots, 501 x 10 pots, 520 x 11 pots, 287 x 12 pots, 182 x 13 pots, 29 x 14 pots, 8 x 15 pots,
24 …………….. 2898 ways: 1 x 6 pots, 12 x 7 pots, 151 x 8 pots, 311 x 9 pots, 647 x 10 pots, 745 x 11 pots, 526 x 12 pots, 379 x 13 pots, 90 x 14 pots, 35 x 15 pots, 1 x 16 pots,
25 …………….. 4148 ways: 1 x 5 pots, 6 x 7 pots, 125 x 8 pots, 292 x 9 pots, 782 x 10 pots, 995 x 11 pots, 882 x 12 pots, 713 x 13 pots, 231 x 14 pots, 112 x 15 pots, 8 x 16 pots, 1 x 17 pots,
26 …………….. 5938 ways: 2 x 7 pots, 95 x 8 pots, 257 x 9 pots, 885 x 10 pots, 1247 x 11 pots, 1367 x 12 pots, 1227 x 13 pots, 518 x 14 pots, 294 x 15 pots, 37 x 16 pots, 9 x 17 pots,
27 …………….. 8501 ways: 1 x 6 pots, 1 x 7 pots, 66 x 8 pots, 211 x 9 pots, 941 x 10 pots, 1466 x 11 pots, 1975 x 12 pots, 1952 x 13 pots, 1043 x 14 pots, 673 x 15 pots, 127 x 16 pots, 44 x 17 pots, 1 x 18 pots,
28 …………….. 12164 ways: 1 x 7 pots, 41 x 8 pots, 160 x 9 pots, 941 x 10 pots, 1619 x 11 pots, 2677 x 12 pots, 2897 x 13 pots, 1919 x 14 pots, 1385 x 15 pots, 358 x 16 pots, 156 x 17 pots, 9 x 18 pots, 1 x 19 pots,
29 …………….. 17410 ways: 23 x 8 pots, 110 x 9 pots, 885 x 10 pots, 1686 x 11 pots, 3416 x 12 pots, 4039 x 13 pots, 3264 x 14 pots, 2605 x 15 pots, 876 x 16 pots, 450 x 17 pots, 46 x 18 pots, 10 x 19 pots,
30 …………….. 24924 ways: 12 x 8 pots, 70 x 9 pots, 782 x 10 pots, 1658 x 11 pots, 4117 x 12 pots, 5308 x 13 pots, 5178 x 14 pots, 4530 x 15 pots, 1918 x 16 pots, 1123 x 17 pots, 173 x 18 pots, 54 x 19 pots, 1 x 20 pots,
31 …………….. 35674 ways: 5 x 8 pots, 42 x 9 pots, 647 x 10 pots, 1538 x 11 pots, 4697 x 12 pots, 6592 x 13 pots, 7714 x 14 pots, 7350 x 15 pots, 3830 x 16 pots, 2507 x 17 pots, 531 x 18 pots, 210 x 19 pots, 10 x 20 pots, 1 x 21 pots,
32 …………….. 51058 ways: 2 x 8 pots, 22 x 9 pots, 501 x 10 pots, 1341 x 11 pots, 5081 x 12 pots, 7758 x 13 pots, 10843 x 14 pots, 11207 x 15 pots, 7065 x 16 pots, 5104 x 17 pots, 1407 x 18 pots, 660 x 19 pots, 56 x 20 pots, 11 x 21 pots,
33 …………….. 73084 ways: 1 x 8 pots, 10 x 9 pots, 362 x 10 pots, 1100 x 11 pots, 5216 x 12 pots, 8671 x 13 pots, 14434 x 14 pots, 16136 x 15 pots, 12153 x 16 pots, 9599 x 17 pots, 3324 x 18 pots, 1783 x 19 pots, 229 x 20 pots, 65 x 21 pots, 1 x 22 pots,
34 …………….. 104611 ways: 1 x 8 pots, 4 x 9 pots, 242 x 10 pots, 850 x 11 pots, 5081 x 12 pots, 9214 x 13 pots, 18249 x 14 pots, 22015 x 15 pots, 19636 x 16 pots, 16837 x 17 pots, 7146 x 18 pots, 4289 x 19 pots, 760 x 20 pots, 275 x 21 pots, 11 x 22 pots, 1 x 23 pots,
35 …………….. 149731 ways: 1 x 8 pots, 2 x 9 pots, 149 x 10 pots, 615 x 11 pots, 4697 x 12 pots, 9308 x 13 pots, 21963 x 14 pots, 28546 x 15 pots, 29961 x 16 pots, 27750 x 17 pots, 14174 x 18 pots, 9384 x 19 pots, 2167 x 20 pots, 935 x 21 pots, 67 x 22 pots, 12 x 23 pots,
36 …………….. 214314 ways: 1 x 9 pots, 84 x 10 pots, 414 x 11 pots, 4118 x 12 pots, 8942 x 13 pots, 25204 x 14 pots, 35265 x 15 pots, 43352 x 16 pots, 43213 x 17 pots, 26200 x 18 pots, 18939 x 19 pots, 5490 x 20 pots, 2718 x 21 pots, 296 x 22 pots, 77 x 23 pots, 1 x 24 pots,
37 …………….. 306761 ways: 44 x 10 pots, 258 x 11 pots, 3419 x 12 pots, 8173 x 13 pots, 27608 x 14 pots, 41582 x 15 pots, 59682 x 16 pots, 63843 x 17 pots, 45478 x 18 pots, 35620 x 19 pots, 12627 x 20 pots, 7006 x 21 pots, 1056 x 22 pots, 352 x 23 pots, 12 x 24 pots, 1 x 25 pots,
38 …………….. 439082 ways: 22 x 10 pots, 150 x 11 pots, 2683 x 12 pots, 7102 x 13 pots, 28889 x 14 pots, 46851 x 15 pots, 78381 x 16 pots, 89784 x 17 pots, 74563 x 18 pots, 62920 x 19 pots, 26755 x 20 pots, 16380 x 21 pots, 3223 x 22 pots, 1287 x 23 pots, 79 x 24 pots, 13 x 25 pots,
39 …………….. 628472 ways: 10 x 10 pots, 81 x 11 pots, 1985 x 12 pots, 5858 x 13 pots, 28890 x 14 pots, 50485 x 15 pots, 98407 x 16 pots, 120519 x 17 pots, 115997 x 18 pots, 105010 x 19 pots, 52782 x 20 pots, 35265 x 21 pots, 8712 x 22 pots, 4005 x 23 pots, 375 x 24 pots, 90 x 25 pots, 1 x 26 pots,
40 …………….. 899559 ways: 5 x 10 pots, 39 x 11 pots, 1382 x 12 pots, 4578 x 13 pots, 27612 x 14 pots, 52066 x 15 pots, 118301 x 16 pots, 154751 x 17 pots, 171849 x 18 pots, 166346 x 19 pots, 97729 x 20 pots, 70675 x 21 pots, 21329 x 22 pots, 11010 x 23 pots, 1431 x 24 pots, 442 x 25 pots, 13 x 26 pots, 1 x 27 pots,
41 …………….. 1287583 ways: 3 x 10 pots, 17 x 11 pots, 903 x 12 pots, 3387 x 13 pots, 25214 x 14 pots, 51410 x 15 pots, 136347 x 16 pots, 190395 x 17 pots, 243165 x 18 pots, 251026 x 19 pots, 170885 x 20 pots, 132935 x 21 pots, 48028 x 22 pots, 27379 x 23 pots, 4654 x 24 pots, 1729 x 25 pots, 92 x 26 pots, 14 x 27 pots,
42 …………….. 1842971 ways: 2 x 10 pots, 7 x 11 pots, 551 x 12 pots, 2368 x 13 pots, 21983 x 14 pots, 48597 x 15 pots, 150803 x 16 pots, 224744 x 17 pots, 329419 x 18 pots, 361946 x 19 pots, 283558 x 20 pots, 236162 x 21 pots, 100581 x 22 pots, 62579 x 23 pots, 13365 x 24 pots, 5734 x 25 pots, 467 x 26 pots, 104 x 27 pots, 1 x 28 pots,
43 …………….. 2637919 ways: 1 x 10 pots, 3 x 11 pots, 314 x 12 pots, 1557 x 13 pots, 18284 x 14 pots, 43961 x 15 pots, 160166 x 16 pots, 254795 x 17 pots, 428084 x 18 pots, 499860 x 19 pots, 448261 x 20 pots, 398219 x 21 pots, 197550 x 22 pots, 132979 x 23 pots, 34683 x 24 pots, 16743 x 25 pots, 1898 x 26 pots, 546 x 27 pots, 14 x 28 pots, 1 x 29 pots,
44 …………….. 3775771 ways: 1 x 11 pots, 168 x 12 pots, 959 x 13 pots, 14490 x 14 pots, 38040 x 15 pots, 163417 x 16 pots, 277659 x 17 pots, 534470 x 18 pots, 662505 x 19 pots, 677252 x 20 pots, 639861 x 21 pots, 366268 x 22 pots, 264979 x 23 pots, 82644 x 24 pots, 44110 x 25 pots, 6552 x 26 pots, 2275 x 27 pots, 106 x 28 pots, 15 x 29 pots,
45 …………….. 5404428 ways: 86 x 12 pots, 552 x 13 pots, 10923 x 14 pots, 31466 x 15 pots, 160196 x 16 pots, 290991 x 17 pots, 641921 x 18 pots, 844036 x 19 pots, 980471 x 20 pots, 982868 x 21 pots, 644336 x 22 pots, 498423 x 23 pots, 182929 x 24 pots, 106612 x 25 pots, 19916 x 26 pots, 8009 x 27 pots, 573 x 28 pots, 119 x 29 pots, 1 x 30 pots,
46 …………….. 7735585 ways: 43 x 12 pots, 297 x 13 pots, 7818 x 14 pots, 24850 x 15 pots, 150872 x 16 pots, 293370 x 17 pots, 742405 x 18 pots, 1034988 x 19 pots, 1363077 x 20 pots, 1447108 x 21 pots, 1079970 x 22 pots, 889636 x 23 pots, 379423 x 24 pots, 239239 x 25 pots, 54587 x 26 pots, 24751 x 27 pots, 2471 x 28 pots, 665 x 29 pots, 15 x 30 pots,
47 …………….. 11072260 ways: 21 x 12 pots, 148 x 13 pots, 5303 x 14 pots, 18707 x 15 pots, 136473 x 16 pots, 284559 x 17 pots, 827441 x 18 pots, 1222863 x 19 pots, 1822984 x 20 pots, 2046693 x 21 pots, 1730467 x 22 pots, 1513117 x 23 pots, 742468 x 24 pots, 502931 x 25 pots, 137152 x 26 pots, 68848 x 27 pots, 9023 x 28 pots, 2940 x 29 pots, 121 x 30 pots, 1 x 31 pots,
48 …………….. 15848110 ways: 11 x 12 pots, 67 x 13 pots, 3404 x 14 pots, 13401 x 15 pots, 118506 x 16 pots, 265540 x 17 pots, 889230 x 18 pots, 1393335 x 19 pots, 2348908 x 20 pots, 2785719 x 21 pots, 2658156 x 22 pots, 2460720 x 23 pots, 1378092 x 24 pots, 997349 x 25 pots, 319706 x 26 pots, 175370 x 27 pots, 28938 x 28 pots, 10949 x 29 pots, 694 x 30 pots, 15 x 31 pots,
49 …………….. 22683561 ways: 6 x 12 pots, 28 x 13 pots, 2065 x 14 pots, 9120 x 15 pots, 98712 x 16 pots, 238324 x 17 pots, 921801 x 18 pots, 1531954 x 19 pots, 2919464 x 20 pots, 3654361 x 21 pots, 3923504 x 22 pots, 3837153 x 23 pots, 2436733 x 24 pots, 1875975 x 25 pots, 697698 x 26 pots, 414167 x 27 pots, 83512 x 28 pots, 35699 x 29 pots, 3165 x 30 pots, 120 x 31 pots,
50 …………….. 32465737 ways: 3 x 12 pots, 11 x 13 pots, 1183 x 14 pots, 5881 x 15 pots, 78801 x 16 pots, 205621 x 17 pots, 921927 x 18 pots, 1626118 x 19 pots, 3503740 x 20 pots, 4626198 x 21 pots, 5575603 x 22 pots, 5750911 x 23 pots, 4119172 x 24 pots, 3361713 x 25 pots, 1435512 x 26 pots, 915369 x 27 pots, 220572 x 28 pots, 104533 x 29 pots, 12188 x 30 pots, 680 x 31 pots, 1 x 32 pots,
51 …………….. 46461613 ways: 1 x 12 pots, 4 x 13 pots, 643 x 14 pots, 3580 x 15 pots, 60222 x 16 pots, 170425 x 17 pots, 889630 x 18 pots, 1666914 x 19 pots, 4063551 x 20 pots, 5657587 x 21 pots, 7640953 x 22 pots, 8300468 x 23 pots, 6676747 x 24 pots, 5759854 x 25 pots, 2800239 x 26 pots, 1906984 x 27 pots, 539811 x 28 pots, 279799 x 29 pots, 41125 x 30 pots, 3061 x 31 pots, 15 x 32 pots,
52 …………….. 66476958 ways: 1 x 13 pots, 335 x 14 pots, 2051 x 15 pots, 44003 x 16 pots, 135584 x 17 pots, 828176 x 18 pots, 1650443 x 19 pots, 4557268 x 20 pots, 6689681 x 21 pots, 10112156 x 22 pots, 11556610 x 23 pots, 10402701 x 24 pots, 9464028 x 25 pots, 5202289 x 26 pots, 3766216 x 27 pots, 1235611 x 28 pots, 693420 x 29 pots, 124623 x 30 pots, 11642 x 31 pots, 120 x 32 pots,
53 …………….. 95077305 ways: 170 x 14 pots, 1103 x 15 pots, 30696 x 16 pots, 103425 x 17 pots, 743560 x 18 pots, 1578405 x 19 pots, 4944725 x 20 pots, 7653294 x 21 pots, 12938644 x 22 pots, 15542947 x 23 pots, 15612036 x 24 pots, 14949960 x 25 pots, 9238817 x 26 pots, 7083819 x 27 pots, 2664571 x 28 pots, 1606514 x 29 pots, 345089 x 30 pots, 38850 x 31 pots, 680 x 32 pots,
54 …………….. 135890756 ways: 85 x 14 pots, 555 x 15 pots, 20416 x 16 pots, 75539 x 17 pots, 643586 x 18 pots, 1457839 x 19 pots, 5192434 x 20 pots, 8476172 x 21 pots, 16021724 x 22 pots, 20217666 x 23 pots, 22608653 x 24 pots, 22752005 x 25 pots, 15732635 x 26 pots, 12737061 x 27 pots, 5444894 x 28 pots, 3505489 x 29 pots, 884327 x 30 pots, 116615 x 31 pots, 3060 x 32 pots, 1 x 33 pots,
55 …………….. 194015321 ways: 42 x 14 pots, 259 x 15 pots, 12933 x 16 pots, 52740 x 17 pots, 536717 x 18 pots, 1300053 x 19 pots, 5278205 x 20 pots, 9091627 x 21 pots, 19215915 x 22 pots, 25460239 x 23 pots, 31640839 x 24 pots, 33418979 x 25 pots, 25755913 x 26 pots, 21961850 x 27 pots, 10592596 x 28 pots, 7246954 x 29 pots, 2117467 x 30 pots, 320350 x 31 pots, 11628 x 32 pots, 15 x 33 pots,
56 …………….. 276554726 ways: 21 x 14 pots, 111 x 15 pots, 7800 x 16 pots, 35136 x 17 pots, 430940 x 18 pots, 1118919 x 19 pots, 5194324 x 20 pots, 9447169 x 21 pots, 22337656 x 22 pots, 31066840 x 23 pots, 42849016 x 24 pots, 47448809 x 25 pots, 40625481 x 26 pots, 36408879 x 27 pots, 19694261 x 28 pots, 14261925 x 29 pots, 4773015 x 30 pots, 815558 x 31 pots, 38746 x 32 pots, 120 x 33 pots,
57 …………….. 393304337 ways: 10 x 14 pots, 44 x 15 pots, 4481 x 16 pots, 22290 x 17 pots, 332850 x 18 pots, 928918 x 19 pots, 4948680 x 20 pots, 9511673 x 21 pots, 25181182 x 22 pots, 36757293 x 23 pots, 56212584 x 24 pots, 65205755 x 25 pots, 61856042 x 26 pots, 58163535 x 27 pots, 35107190 x 28 pots, 26823616 x 29 pots, 10188971 x 30 pots, 1942474 x 31 pots, 116069 x 32 pots, 680 x 33 pots,
58 …………….. 557600883 ways: 4 x 14 pots, 16 x 15 pots, 2458 x 16 pots, 13429 x 17 pots, 247071 x 18 pots, 743334 x 19 pots, 4563596 x 20 pots, 9279772 x 21 pots, 27539923 x 22 pots, 42194559 x 23 pots, 71504995 x 24 pots, 86828841 x 25 pots, 91060148 x 26 pots, 89706539 x 27 pots, 60165405 x 28 pots, 48371299 x 29 pots, 20698055 x 30 pots, 4360304 x 31 pots, 318075 x 32 pots, 3060 x 33 pots,
59 …………….. 787334076 ways: 1 x 14 pots, 5 x 15 pots, 1296 x 16 pots, 7659 x 17 pots, 176070 x 18 pots, 572849 x 19 pots, 4072609 x 20 pots, 8772573 x 21 pots, 29230507 x 22 pots, 47015530 x 23 pots, 88267048 x 24 pots, 112144770 x 25 pots, 129789992 x 26 pots, 133793635 x 27 pots, 99355374 x 28 pots, 83864809 x 29 pots, 40171744 x 30 pots, 9278426 x 31 pots, 807550 x 32 pots, 11628 x 33 pots, 1 x 34 pots,
60 …………….. 1106093149 ways: 1 x 15 pots, 663 x 16 pots, 4123 x 17 pots, 120329 x 18 pots, 424714 x 19 pots, 3515829 x 20 pots, 8034577 x 21 pots, 30115636 x 22 pots, 50869616 x 23 pots, 105807277 x 24 pots, 140601595 x 25 pots, 179325829 x 26 pots, 193239536 x 27 pots, 158411177 x 28 pots, 140121360 x 29 pots, 74739123 x 30 pots, 18805268 x 31 pots, 1917736 x 32 pots, 38745 x 33 pots, 15 x 34 pots,
61 …………….. 1544385532 ways: 332 x 16 pots, 2088 x 17 pots, 78784 x 18 pots, 302559 x 19 pots, 2934724 x 20 pots, 7127468 x 21 pots, 30121964 x 22 pots, 53459707 x 23 pots, 123235044 x 24 pots, 171239544 x 25 pots, 240428123 x 26 pots, 270604349 x 27 pots, 244269036 x 28 pots, 226061683 x 29 pots, 133668917 x 30 pots, 36443487 x 31 pots, 4291548 x 32 pots, 116055 x 33 pots, 120 x 34 pots,
62 …………….. 2140819199 ways: 163 x 16 pots, 990 x 17 pots, 49384 x 18 pots, 206793 x 19 pots, 2367234 x 20 pots, 6121912 x 21 pots, 29249848 x 22 pots, 54578986 x 23 pots, 139526907 x 24 pots, 202712127 x 25 pots, 313083135 x 26 pots, 367799159 x 27 pots, 364820211 x 28 pots, 352771499 x 29 pots, 230359720 x 30 pots, 67748957 x 31 pots, 9103523 x 32 pots, 317971 x 33 pots, 680 x 34 pots,
63 …………….. 2943088267 ways: 78 x 16 pots, 436 x 17 pots, 29631 x 18 pots, 135377 x 19 pots, 1843977 x 20 pots, 5088787 x 21 pots, 27573243 x 22 pots, 54137391 x 23 pots, 153620819 x 24 pots, 233364077 x 25 pots, 396281759 x 26 pots, 485648749 x 27 pots, 528413405 x 28 pots, 533273974 x 29 pots, 383326003 x 30 pots, 121147498 x 31 pots, 18392999 x 32 pots, 807004 x 33 pots, 3060 x 34 pots,
64 …………….. 4008549527 ways: 36 x 16 pots, 177 x 17 pots, 17030 x 18 pots, 84725 x 19 pots, 1386044 x 20 pots, 4091293 x 21 pots, 25229762 x 22 pots, 52173232 x 23 pots, 164526868 x 24 pots, 261363545 x 25 pots, 487875964 x 26 pots, 623469314 x 27 pots, 743085615 x 28 pots, 781916473 x 29 pots, 617002443 x 30 pots, 208865247 x 31 pots, 35534670 x 32 pots, 1915461 x 33 pots, 11628 x 34 pots,
65 …………….. 5404135175 ways: 15 x 16 pots, 66 x 17 pots, 9393 x 18 pots, 50579 x 19 pots, 1004488 x 20 pots, 3179167 x 21 pots, 22402672 x 22 pots, 48847975 x 23 pots, 171439060 x 24 pots, 284875691 x 25 pots, 584553855 x 26 pots, 778732632 x 27 pots, 1015543269 x 28 pots, 1113306753 x 29 pots, 962128393 x 30 pots, 347876991 x 31 pots, 65861890 x 32 pots, 4283540 x 33 pots, 38745 x 34 pots, 1 x 35 pots,
66 …………….. 7205326681 ways: 5 x 16 pots, 22 x 17 pots, 4990 x 18 pots, 28725 x 19 pots, 701269 x 20 pots, 2385626 x 21 pots, 19297969 x 22 pots, 44425089 x 23 pots, 173831121 x 24 pots, 302255789 x 25 pots, 681962090 x 26 pots, 946890954 x 27 pots, 1349968986 x 28 pots, 1540791967 x 29 pots, 1455434608 x 30 pots, 560716734 x 31 pots, 117435882 x 32 pots, 9078785 x 33 pots, 116055 x 34 pots, 15 x 35 pots,
67 …………….. 9493929976 ways: 1 x 16 pots, 6 x 17 pots, 2568 x 18 pots, 15473 x 19 pots, 471228 x 20 pots, 1727017 x 21 pots, 16120417 x 22 pots, 39236610 x 23 pots, 171520960 x 24 pots, 312234462 x 25 pots, 774983963 x 26 pots, 1121425658 x 27 pots, 1746784802 x 28 pots, 2074554742 x 29 pots, 2138354818 x 30 pots, 875936248 x 31 pots, 201918670 x 32 pots, 18324243 x 33 pots, 317970 x 34 pots, 120 x 35 pots,
68 …………….. 12354454273 ways: 1 x 17 pots, 1287 x 18 pots, 7880 x 19 pots, 304551 x 20 pots, 1204747 x 21 pots, 13052296 x 22 pots, 33643204 x 23 pots, 164693125 x 24 pots, 314066907 x 25 pots, 858155975 x 26 pots, 1294156579 x 27 pots, 2201548665 x 28 pots, 2719493739 x 29 pots, 3054542713 x 30 pots, 1327955087 x 31 pots, 335460079 x 32 pots, 35359768 x 33 pots, 806990 x 34 pots, 680 x 35 pots,
69 …………….. 15869012941 ways: 629 x 18 pots, 3779 x 19 pots, 189212 x 20 pots, 808758 x 21 pots, 10237736 x 22 pots, 27994253 x 23 pots, 153875458 x 24 pots, 307622380 x 25 pots, 926179819 x 26 pots, 1455810773 x 27 pots, 2704184926 x 28 pots, 3473145157 x 29 pots, 4246100522 x 30 pots, 1956037164 x 31 pots, 539454324 x 32 pots, 65449634 x 33 pots, 1915357 x 34 pots, 3060 x 35 pots,
70 …………….. 20110834570 ways: 298 x 18 pots, 1697 x 19 pots, 112996 x 20 pots, 521672 x 21 pots, 7774240 x 22 pots, 22593802 x 23 pots, 139873911 x 24 pots, 293399283 x 25 pots, 974465735 x 26 pots, 1596805691 x 27 pots, 3238740766 x 28 pots, 4323966466 x 29 pots, 5748616288 x 30 pots, 2802171243 x 31 pots, 840968705 x 32 pots, 116527155 x 33 pots, 4282994 x 34 pots, 11628 x 35 pots,
71 …………….. 25136684168 ways: 135 x 18 pots, 708 x 19 pots, 64899 x 20 pots, 322759 x 21 pots, 5711557 x 22 pots, 17676637 x 23 pots, 123676359 x 24 pots, 272463501 x 25 pots, 999631953 x 26 pots, 1708160471 x 27 pots, 3783813606 x 28 pots, 5250323886 x 29 pots, 7585344742 x 30 pots, 3907736677 x 31 pots, 1272608978 x 32 pots, 200032045 x 33 pots, 9076510 x 34 pots, 38745 x 35 pots,
72 …………….. 30978724607 ways: 57 x 18 pots, 272 x 19 pots, 35897 x 20 pots, 191161 x 21 pots, 4056792 x 22 pots, 13396608 x 23 pots, 106340852 x 24 pots, 246320363 x 25 pots, 999886592 x 26 pots, 1782418774 x 27 pots, 4313711666 x 28 pots, 6220485910 x 29 pots, 9761116263 x 30 pots, 5309002141 x 31 pots, 1871578777 x 32 pots, 331750191 x 33 pots, 18316235 x 34 pots, 116055 x 35 pots, 1 x 36 pots,
73 …………….. 37636563655 ways: 21 x 18 pots, 95 x 19 pots, 19165 x 20 pots, 108133 x 21 pots, 2783744 x 22 pots, 9826987 x 23 pots, 88885330 x 24 pots, 216740933 x 25 pots, 975233635 x 26 pots, 1814454512 x 27 pots, 4800301437 x 28 pots, 7193822287 x 29 pots, 12256771414 x 30 pots, 7031720554 x 31 pots, 2677728926 x 32 pots, 532513467 x 33 pots, 35335030 x 34 pots, 317970 x 35 pots, 15 x 36 pots,
74 …………….. 45070392894 ways: 6 x 18 pots, 29 x 19 pots, 9907 x 20 pots, 58262 x 21 pots, 1844155 x 22 pots, 6970579 x 23 pots, 72194215 x 24 pots, 185569595 x 25 pots, 927470934 x 26 pots, 1802042322 x 27 pots, 5215379535 x 28 pots, 8123250126 x 29 pots, 15025041751 x 30 pots, 9085318582 x 31 pots, 3730486475 x 32 pots, 828568433 x 33 pots, 65380878 x 34 pots, 806990 x 35 pots, 120 x 36 pots,
75 …………….. 53196190853 ways: 1 x 18 pots, 7 x 19 pots, 4974 x 20 pots, 29809 x 21 pots, 1178783 x 22 pots, 4776114 x 23 pots, 56953038 x 24 pots, 154541114 x 25 pots, 859980665 x 26 pots, 1746106896 x 27 pots, 5533304037 x 28 pots, 8958777946 x 29 pots, 17988784431 x 30 pots, 11457391195 x 31 pots, 5064703410 x 32 pots, 1251390144 x 33 pots, 116352253 x 34 pots, 1915356 x 35 pots, 680 x 36 pots,
76 …………….. 61883900927 ways: 1 x 19 pots, 2427 x 20 pots, 14431 x 21 pots, 726720 x 22 pots, 3157230 x 23 pots, 43616365 x 24 pots, 125131491 x 25 pots, 777345035 x 26 pots, 1650613367 x 27 pots, 5733553709 x 28 pots, 9651806800 x 29 pots, 21042301066 x 30 pots, 14109351520 x 31 pots, 6705659286 x 32 pots, 1836715650 x 33 pots, 199619789 x 34 pots, 4282980 x 35 pots, 3060 x 36 pots,
77 …………….. 70959289848 ways: 1146 x 20 pots, 6580 x 21 pots, 432076 x 22 pots, 2010745 x 23 pots, 32408224 x 24 pots, 98458866 x 25 pots, 684846125 x 26 pots, 1522116055 x 27 pots, 5802868668 x 28 pots, 10159692543 x 29 pots, 24056131936 x 30 pots, 16974108157 x 31 pots, 8663664804 x 32 pots, 2622614425 x 33 pots, 330841465 x 34 pots, 9076405 x 35 pots, 11628 x 36 pots,
78 …………….. 80209851969 ways: 518 x 20 pots, 2808 x 21 pots, 247838 x 22 pots, 1231796 x 23 pots, 23349271 x 24 pots, 75240727 x 25 pots, 587923705 x 26 pots, 1369034789 x 27 pots, 5736669514 x 28 pots, 10449988666 x 29 pots, 26885251047 x 30 pots, 19956515326 x 31 pots, 10928906953 x 32 pots, 3646507736 x 33 pots, 530626855 x 34 pots, 18315675 x 35 pots, 38745 x 36 pots,
79 …………….. 89394679675 ways: 220 x 20 pots, 1112 x 21 pots, 137269 x 22 pots, 724555 x 23 pots, 16301751 x 24 pots, 55804155 x 25 pots, 491666159 x 26 pots, 1200766997 x 27 pots, 5539548814 x 28 pots, 10503796342 x 29 pots, 29380063990 x 30 pots, 22937059450 x 31 pots, 13467307027 x 32 pots, 4941194493 x 33 pots, 824858636 x 34 pots, 35332650 x 35 pots, 116055 x 36 pots,
80 …………….. 98257725552 ways: 85 x 20 pots, 404 x 21 pots, 73516 x 22 pots, 408376 x 23 pots, 11022270 x 24 pots, 40138263 x 25 pots, 400398024 x 26 pots, 1026762362 x 27 pots, 5224762986 x 28 pots, 10317751926 x 29 pots, 31399119052 x 30 pots, 25778834437 x 31 pots, 16218189616 x 32 pots, 6530124213 x 33 pots, 1244449742 x 34 pots, 65372310 x 35 pots, 317970 x 36 pots,
81 …………….. 106543410369 ways: 28 x 20 pots, 132 x 21 pots, 38137 x 22 pots, 220023 x 23 pots, 7213316 x 24 pots, 27973451 x 25 pots, 317406443 x 26 pots, 855682726 x 27 pots, 4812800099 x 28 pots, 9904367941 x 29 pots, 32822076900 x 30 pots, 28337373991 x 31 pots, 19094455165 x 32 pots, 8422352694 x 33 pots, 1824317198 x 34 pots, 116325135 x 35 pots, 806990 x 36 pots,
82 …………….. 114013159080 ways: 7 x 20 pots, 37 x 21 pots, 19192 x 22 pots, 113002 x 23 pots, 4566841 x 24 pots, 18871019 x 25 pots, 244822864 x 26 pots, 694745948 x 27 pots, 4329232623 x 28 pots, 9290680426 x 29 pots, 33561324277 x 30 pots, 30472432318 x 31 pots, 21985703941 x 32 pots, 10607786985 x 33 pots, 2601401779 x 34 pots, 199542465 x 35 pots, 1915356 x 36 pots,
83 …………….. 120461240151 ways: 1 x 20 pots, 8 x 21 pots, 9370 x 22 pots, 55144 x 23 pots, 2796202 x 24 pots, 12308816 x 25 pots, 183650919 x 26 pots, 549314616 x 27 pots, 3802159713 x 28 pots, 8515400466 x 29 pots, 33570707728 x 30 pots, 32060422408 x 31 pots, 24764395570 x 32 pots, 13053433605 x 33 pots, 3611663160 x 34 pots, 330639445 x 35 pots, 4282980 x 36 pots,
84 …………….. 125728284654 ways: 1 x 21 pots, 4424 x 22 pots, 25467 x 23 pots, 1655556 x 24 pots, 7752725 x 25 pots, 133911197 x 26 pots, 422746953 x 27 pots, 3259585491 x 28 pots, 7624976296 x 29 pots, 32850203790 x 30 pots, 33006012403 x 31 pots, 27294693859 x 32 pots, 15701372601 x 33 pots, 4886130211 x 34 pots, 530137275 x 35 pots, 9076405 x 36 pots,
85 …………….. 129711082879 ways: 2004 x 22 pots, 11073 x 23 pots, 948028 x 24 pots, 4708497 x 25 pots, 94861673 x 26 pots, 316486481 x 27 pots, 2727063320 x 28 pots, 6669108877 x 29 pots, 31445882704 x 30 pots, 33251397739 x 31 pots, 29443210930 x 32 pots, 18469067727 x 33 pots, 6446270261 x 34 pots, 823747890 x 35 pots, 18315675 x 36 pots,
86 …………….. 132367672343 ways: 859 x 22 pots, 4501 x 23 pots, 525322 x 24 pots, 2752896 x 25 pots, 65249651 x 26 pots, 230336431 x 27 pots, 2225868114 x 28 pots, 5696307438 x 29 pots, 29445173749 x 30 pots, 32782021390 x 31 pots, 31090506202 x 32 pots, 21252387798 x 33 pots, 8299131792 x 34 pots, 1242073550 x 35 pots, 35332650 x 36 pots,
87 …………….. 133717280974 ways: 341 x 22 pots, 1694 x 23 pots, 281908 x 24 pots, 1546567 x 25 pots, 43555936 x 26 pots, 162848429 x 27 pots, 1771855606 x 28 pots, 4750019602 x 29 pots, 26968089726 x 30 pots, 31627972222 x 31 pots, 32141986345 x 32 pots, 23931378735 x 33 pots, 10432874898 x 34 pots, 1819496655 x 35 pots, 65372310 x 36 pots,
88 …………….. 133835290090 ways: 121 x 22 pots, 582 x 23 pots, 146643 x 24 pots, 833085 x 25 pots, 28202213 x 26 pots, 111752771 x 27 pots, 1375051120 x 28 pots, 3865739086 x 29 pots, 24155604232 x 30 pots, 29860878427 x 31 pots, 32536841857 x 32 pots, 26378436504 x 33 pots, 12813393129 x 34 pots, 2592085185 x 35 pots, 116325135 x 36 pots,
89 …………….. 132843944268 ways: 36 x 22 pots, 178 x 23 pots, 73986 x 24 pots, 429210 x 25 pots, 17705265 x 26 pots, 74367404 x 27 pots, 1039902747 x 28 pots, 3069313155 x 29 pots, 21156709360 x 30 pots, 27586730149 x 31 pots, 32253859756 x 32 pots, 28468150857 x 33 pots, 15382715535 x 34 pots, 3594444165 x 35 pots, 199542465 x 36 pots,
90 …………….. 130899976956 ways: 8 x 22 pots, 46 x 23 pots, 36190 x 24 pots, 210881 x 25 pots, 10773857 x 26 pots, 47940520 x 27 pots, 766052240 x 28 pots, 2376478858 x 29 pots, 18115764867 x 30 pots, 24935607430 x 31 pots, 31313345182 x 32 pots, 30087785886 x 33 pots, 18059740575 x 34 pots, 4855600971 x 35 pots, 330639445 x 36 pots,
91 …………….. 128180581099 ways: 1 x 22 pots, 9 x 23 pots, 17119 x 24 pots, 98461 x 25 pots, 6353659 x 26 pots, 29902586 x 27 pots, 549431589 x 28 pots, 1793485681 x 29 pots, 15161583364 x 30 pots, 22049665840 x 31 pots, 29774905657 x 32 pots, 31147195197 x 33 pots, 20743597971 x 34 pots, 6394206690 x 35 pots, 530137275 x 36 pots,
92 …………….. 124869206939 ways: 1 x 23 pots, 7785 x 24 pots, 43495 x 25 pots, 3631443 x 26 pots, 18022980 x 27 pots, 383485935 x 28 pots, 1318538469 x 29 pots, 12399326398 x 30 pots, 19070885749 x 31 pots, 27731413429 x 32 pots, 31586975538 x 33 pots, 23319589557 x 34 pots, 8213538270 x 35 pots, 823747890 x 36 pots,
93 …………….. 121142526449 ways: 3369 x 24 pots, 18074 x 25 pots, 2012077 x 26 pots, 10481136 x 27 pots, 260348595 x 28 pots, 943732036 x 29 pots, 9905793147 x 30 pots, 16130009641 x 31 pots, 25299968686 x 32 pots, 31383851085 x 33 pots, 25667277678 x 34 pots, 10296957375 x 35 pots, 1242073550 x 36 pots,
94 …………….. 117159607643 ways: 1366 x 24 pots, 7010 x 25 pots, 1081168 x 26 pots, 5871100 x 27 pots, 171840581 x 28 pots, 657148141 x 29 pots, 7728161416 x 30 pots, 13337805550 x 31 pots, 22611055018 x 32 pots, 30552625326 x 33 pots, 27669935607 x 34 pots, 12604578705 x 35 pots, 1819496655 x 36 pots,
95 …………….. 113053954684 ways: 507 x 24 pots, 2510 x 25 pots, 563631 x 26 pots, 3161699 x 27 pots, 110222373 x 28 pots, 444834690 x 29 pots, 5885779237 x 30 pots, 10779368161 x 31 pots, 19797251467 x 32 pots, 29144483865 x 33 pots, 29224315434 x 34 pots, 15071885925 x 35 pots, 2592085185 x 36 pots,
96 …………….. 108928662945 ways: 166 x 24 pots, 816 x 25 pots, 285092 x 26 pots, 1633206 x 27 pots, 68678514 x 28 pots, 292467397 x 29 pots, 4374272226 x 30 pots, 8511686314 x 31 pots, 16982824123 x 32 pots, 27241906956 x 33 pots, 30249578295 x 34 pots, 17610885675 x 35 pots, 3594444165 x 36 pots,
97 …………….. 104854577935 ways: 45 x 24 pots, 234 x 25 pots, 139815 x 26 pots, 807131 x 27 pots, 41557469 x 28 pots, 186585726 x 29 pots, 3171061687 x 30 pots, 6564252175 x 31 pots, 14275285912 x 32 pots, 24950877879 x 33 pots, 30694297596 x 34 pots, 20114111295 x 35 pots, 4855600971 x 36 pots,
98 …………….. 100871079992 ways: 9 x 24 pots, 56 x 25 pots, 66336 x 26 pots, 380431 x 27 pots, 24415835 x 28 pots, 115380021 x 29 pots, 2241381313 x 30 pots, 4942132690 x 31 pots, 11759640493 x 32 pots, 22391385126 x 33 pots, 30540683487 x 34 pots, 22461407505 x 35 pots, 6394206690 x 36 pots,
99 …………….. 96988963584 ways: 1 x 24 pots, 10 x 25 pots, 30312 x 26 pots, 170366 x 27 pots, 13927070 x 28 pots, 69072707 x 29 pots, 1544007587 x 30 pots, 3630709759 x 31 pots, 9495589612 x 32 pots, 19687368615 x 33 pots, 29805548100 x 34 pots, 24529001175 x 35 pots, 8213538270 x 36 pots,
100 ………….. 93194837248 ways: 1 x 25 pots, 13238 x 26 pots, 72139 x 27 pots, 7713226 x 28 pots, 39977252 x 29 pots, 1036133467 x 30 pots, 2601232909 x 31 pots, 7517561455 x 32 pots, 16957239654 x 33 pots, 28537972155 x 34 pots, 26199964377 x 35 pots, 10296957375 x 36 pots,
101 ………….. 89456513181 ways: 5462 x 26 pots, 28700 x 27 pots, 4148119 x 28 pots, 22334703 x 29 pots, 677063367 x 30 pots, 1816400121 x 31 pots, 5837077090 x 32 pots, 14305928355 x 33 pots, 26814068454 x 34 pots, 27374880105 x 35 pots, 12604578705 x 36 pots,
102 ………….. 85728946234 ways: 2094 x 26 pots, 10636 x 27 pots, 2166354 x 28 pots, 12023933 x 29 pots, 430641842 x 30 pots, 1235351407 x 31 pots, 4446756250 x 32 pots, 11819121993 x 33 pots, 24729593985 x 34 pots, 27981391815 x 35 pots, 15071885925 x 36 pots,
103 ………….. 81960380375 ways: 728 x 26 pots, 3627 x 27 pots, 1098424 x 28 pots, 6224972 x 29 pots, 266514487 x 30 pots, 817678348 x 31 pots, 3325187101 x 32 pots, 9560010072 x 33 pots, 22391385126 x 34 pots, 27981391815 x 35 pots, 17610885675 x 36 pots,
104 ………….. 78098434728 ways: 221 x 26 pots, 1117 x 27 pots, 540255 x 28 pots, 3091973 x 29 pots, 160440233 x 30 pots, 526275341 x 31 pots, 2441934927 x 32 pots, 7568506752 x 33 pots, 19908652509 x 34 pots, 27374880105 x 35 pots, 20114111295 x 36 pots,
105 ………….. 74095894242 ways: 55 x 26 pots, 301 x 27 pots, 257257 x 28 pots, 1469403 x 29 pots, 93928073 x 30 pots, 329049207 x 31 pots, 1762109263 x 32 pots, 5862630645 x 33 pots, 17385078156 x 34 pots, 26199964377 x 35 pots, 22461407505 x 36 pots,
106 ………….. 69915962164 ways: 10 x 26 pots, 67 x 27 pots, 118170 x 28 pots, 665899 x 29 pots, 53469028 x 30 pots, 199641278 x 31 pots, 1250104783 x 32 pots, 4441520514 x 33 pots, 14912440065 x 34 pots, 24529001175 x 35 pots, 24529001175 x 36 pots,
107 ………….. 65536699199 ways: 1 x 26 pots, 11 x 27 pots, 52055 x 28 pots, 286585 x 29 pots, 29593448 x 30 pots, 117392890 x 31 pots, 872335223 x 32 pots, 3289467885 x 33 pots, 12566199219 x 34 pots, 22461407505 x 35 pots, 26199964377 x 36 pots,
108 ………….. 60954344587 ways: 1 x 27 pots, 21798 x 28 pots, 116520 x 29 pots, 15923635 x 30 pots, 66806561 x 31 pots, 598956949 x 32 pots, 2380350053 x 33 pots, 10403177670 x 34 pots, 20114111295 x 35 pots, 27374880105 x 36 pots,
109 ………….. 56185215951 ways: 8570 x 28 pots, 44448 x 29 pots, 8328579 x 30 pots, 36734478 x 31 pots, 404707750 x 32 pots, 1681929942 x 33 pots, 8461184694 x 34 pots, 17610885675 x 35 pots, 27981391815 x 36 pots,
110 ………….. 51265939837 ways: 3109 x 28 pots, 15759 x 29 pots, 4232515 x 30 pots, 19479785 x 31 pots, 269059431 x 32 pots, 1159623951 x 33 pots, 6760247547 x 34 pots, 15071885925 x 35 pots, 27981391815 x 36 pots,
111 ………….. 46251882479 ways: 1015 x 28 pots, 5124 x 29 pots, 2087959 x 30 pots, 9939996 x 31 pots, 175904264 x 32 pots, 779494345 x 33 pots, 5304990966 x 34 pots, 12604578705 x 35 pots, 27374880105 x 36 pots,
112 ………….. 41213822530 ways: 287 x 28 pots, 1497 x 29 pots, 998105 x 30 pots, 4867838 x 31 pots, 112977841 x 32 pots, 510372075 x 33 pots, 4087683135 x 34 pots, 10296957375 x 35 pots, 26199964377 x 36 pots,
113 ………….. 36233109834 ways: 66 x 28 pots, 380 x 29 pots, 460959 x 30 pots, 2280644 x 31 pots, 71179902 x 32 pots, 325139559 x 33 pots, 3091508879 x 34 pots, 8213538270 x 35 pots, 24529001175 x 36 pots,
114 ………….. 31395751343 ways: 11 x 28 pots, 79 x 29 pots, 204717 x 30 pots, 1018280 x 31 pots, 43905108 x 32 pots, 201289833 x 33 pots, 2293719120 x 34 pots, 6394206690 x 35 pots, 22461407505 x 36 pots,
115 ………….. 26786019116 ways: 1 x 28 pots, 12 x 29 pots, 86834 x 30 pots, 431188 x 31 pots, 26448865 x 32 pots, 120926172 x 33 pots, 1668413778 x 34 pots, 4855600971 x 35 pots, 20114111295 x 36 pots,
116 ………….. 22480253525 ways: 1 x 29 pots, 34845 x 30 pots, 172100 x 31 pots, 15515996 x 32 pots, 70379246 x 33 pots, 1188821497 x 34 pots, 3594444165 x 35 pots, 17610885675 x 36 pots,
117 ………….. 18541517919 ways: 13058 x 30 pots, 64227 x 31 pots, 8834738 x 32 pots, 39605645 x 33 pots, 829029141 x 34 pots, 2592085185 x 35 pots, 15071885925 x 36 pots,
118 ………….. 15015648375 ways: 4489 x 30 pots, 22171 x 31 pots, 4864345 x 32 pots, 21501975 x 33 pots, 565180035 x 34 pots, 1819496655 x 35 pots, 12604578705 x 36 pots,
119 ………….. 11929052119 ways: 1380 x 30 pots, 6973 x 31 pots, 2578971 x 32 pots, 11231950 x 33 pots, 376201920 x 34 pots, 1242073550 x 35 pots, 10296957375 x 36 pots,
120 ………….. 9288373466 ways: 365 x 30 pots, 1954 x 31 pots, 1310380 x 32 pots, 5627533 x 33 pots, 244147074 x 34 pots, 823747890 x 35 pots, 8213538270 x 36 pots,
121 ………….. 7081906488 ways: 78 x 30 pots, 471 x 31 pots, 634614 x 32 pots, 2694162 x 33 pots, 154233198 x 34 pots, 530137275 x 35 pots, 6394206690 x 36 pots,
122 ………….. 5282428323 ways: 12 x 30 pots, 92 x 31 pots, 291075 x 32 pots, 1226801 x 33 pots, 94669927 x 34 pots, 330639445 x 35 pots, 4855600971 x 36 pots,
123 ………….. 3850986987 ways: 1 x 30 pots, 13 x 31 pots, 125467 x 32 pots, 528325 x 33 pots, 56346551 x 34 pots, 199542465 x 35 pots, 3594444165 x 36 pots,
124 ………….. 2741118904 ways: 1 x 31 pots, 50339 x 32 pots, 213648 x 33 pots, 32444596 x 34 pots, 116325135 x 35 pots, 2592085185 x 36 pots,
125 ………….. 1902993900 ways: 18566 x 32 pots, 80384 x 33 pots, 18025985 x 34 pots, 65372310 x 35 pots, 1819496655 x 36 pots,
126 ………….. 1287074751 ways: 6189 x 32 pots, 27798 x 33 pots, 9634564 x 34 pots, 35332650 x 35 pots, 1242073550 x 36 pots,
127 ………….. 847010671 ways: 1820 x 32 pots, 8688 x 33 pots, 4936598 x 34 pots, 18315675 x 35 pots, 823747890 x 36 pots,
128 ………….. 541631467 ways: 455 x 32 pots, 2395 x 33 pots, 2414937 x 34 pots, 9076405 x 35 pots, 530137275 x 36 pots,
129 ………….. 336045451 ways: 91 x 32 pots, 561 x 33 pots, 1122374 x 34 pots, 4282980 x 35 pots, 330639445 x 36 pots,
130 ………….. 201950579 ways: 13 x 32 pots, 105 x 33 pots, 492640 x 34 pots, 1915356 x 35 pots, 199542465 x 36 pots,
131 ………….. 117334840 ways: 1 x 32 pots, 14 x 33 pots, 202700 x 34 pots, 806990 x 35 pots, 116325135 x 36 pots,
132 ………….. 65767725 ways: 1 x 33 pots, 77444 x 34 pots, 317970 x 35 pots, 65372310 x 36 pots,
133 ………….. 35475838 ways: 27133 x 34 pots, 116055 x 35 pots, 35332650 x 36 pots,
134 ………….. 18362989 ways: 8569 x 34 pots, 38745 x 35 pots, 18315675 x 36 pots,
135 ………….. 9090413 ways: 2380 x 34 pots, 11628 x 35 pots, 9076405 x 36 pots,
136 ………….. 4286600 ways: 560 x 34 pots, 3060 x 35 pots, 4282980 x 36 pots,
137 ………….. 1916141 ways: 105 x 34 pots, 680 x 35 pots, 1915356 x 36 pots,
138 ………….. 807124 ways: 14 x 34 pots, 120 x 35 pots, 806990 x 36 pots,
139 ………….. 317986 ways: 1 x 34 pots, 15 x 35 pots, 317970 x 36 pots,
140 ………….. 116056 ways: 1 x 35 pots, 116055 x 36 pots,
141 ………….. 38745 ways: 38745 x 36 pots,
142 ………….. 11628 ways: 11628 x 36 pots,
143 ………….. 3060 ways: 3060 x 36 pots,
144 ………….. 680 ways: 680 x 36 pots,
145 ………….. 120 ways: 120 x 36 pots,
146 ………….. 15 ways: 15 x 36 pots,
147 ………….. 1 way: 1 x 36 pots,

[davis_greatest]

Could you break this down by number of pots?

e.g.:

Break of 1: 1 way, 1 pot
Break of 2: 1 way, 2 pots
Break of 3: 2 ways, 1× 1 pot and 1× 2pots
Break of 4: 3 ways, 1× 1 pot, 1× 2 pots and 1× 3 pots
Break of 5: 5 ways, 1× 1 pot, 2× 2 pots, 2× 3 pots
...
Break of 147: 1 way, 36 pots.

Presumably the break that can be made using the most different numbers of shots would be 72.

I'll see what I can do. I did the calculations all on one sheet for simplicity, rather than breaking them down by number of pots, so I don't currently have this breakdown.

Definitely it is possible - I'll just need to add some more columns to calculate this - once I've finished working later this evening...

[The Statman]

I decided it wasn't as hard as I had thought, so here I think is the answer to your question.

This list includes all "normal" possible breaks, i.e. it excludes:
- 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

etc. etc.

Could you break this down by number of pots?

e.g.:

Break of 1: 1 way, 1 pot
Break of 2: 1 way, 2 pots
Break of 3: 2 ways, 1× 1 pot and 1× 2pots
Break of 4: 3 ways, 1× 1 pot, 1× 2 pots and 1× 3 pots
Break of 5: 5 ways, 1× 1 pot, 2× 2 pots, 2× 3 pots
...
Break of 147: 1 way, 36 pots.

Presumably the break that can be made using the most different numbers of shots would be 72.