Puzzles with numbers and things

[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...

[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.

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]

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...

[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]

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

[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?

[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]

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]

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!

[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:

[abextra]

Good job, guys, very impressive!

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

[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!

[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]

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