solution_9_6

Solution 6

Steps	Marbles left	Ways to solve
23	9	8298930864

Step 0:
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└───┐ ● ● ● ┌───┘
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    └───────┘

Step 1:
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┌───┘ ● ● ● └───┐
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└───┐ ● ● ● ┌───┘
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Step 2:
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Step 3:
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Step 4:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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└───┐ ● ● ● ┌───┘
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    └───────┘

Step 5:
    ┌───────┐
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└───┐ ● ● ● ┌───┘
    │ ● ● ● │
    └───────┘

Step 6:
    ┌───────┐
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┌───┘ ● ○ ○ └───┐
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│ ● ○ ● ● ○ ● ● │
│ ● ● ● ● ● ● ● │
└───┐ ● ● ● ┌───┘
    │ ● ● ● │
    └───────┘

Step 7:
    ┌───────┐
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┌───┘ ● ○ ○ └───┐
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│ ● ○ ● ● ● ○ ○ │
│ ● ● ● ● ● ● ● │
└───┐ ● ● ● ┌───┘
    │ ● ● ● │
    └───────┘

Step 8:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ● ○ ● ● ○ ○ ○ │
│ ● ● ● ● ● ● ● │
└───┐ ● ● ● ┌───┘
    │ ● ● ● │
    └───────┘

Step 9:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ● ○ ● ● ● ○ ○ │
│ ● ● ● ● ○ ● ● │
└───┐ ● ● ○ ┌───┘
    │ ● ● ● │
    └───────┘

Step 10:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
│ ○ ● ○ ○ ○ ● ● │
│ ● ○ ● ● ● ○ ○ │
│ ● ● ● ● ○ ● ● │
└───┐ ● ● ○ ┌───┘
    │ ● ● ● │
    └───────┘

Step 11:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ● ○ ● ● ● ○ ○ │
│ ● ● ● ● ○ ● ● │
└───┐ ● ● ○ ┌───┘
    │ ● ● ● │
    └───────┘

Step 12:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ● ○ ● ● ● ○ ○ │
│ ● ● ● ● ○ ● ● │
└───┐ ○ ○ ● ┌───┘
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    └───────┘

Step 13:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ● ○ ● ● ● ○ ○ │
│ ● ● ● ● ● ○ ○ │
└───┐ ○ ○ ● ┌───┘
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    └───────┘

Step 14:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ○ ○ ● ● ● ○ ○ │
│ ○ ● ● ● ● ○ ○ │
└───┐ ○ ○ ● ┌───┘
    │ ● ● ● │
    └───────┘

Step 15:
    ┌───────┐
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┌───┘ ● ○ ● └───┐
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│ ○ ○ ● ● ● ○ ○ │
│ ○ ● ● ○ ○ ● ○ │
└───┐ ○ ○ ● ┌───┘
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    └───────┘

Step 16:
    ┌───────┐
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┌───┘ ○ ○ ● └───┐
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│ ○ ○ ● ● ● ○ ○ │
│ ○ ● ● ○ ○ ● ○ │
└───┐ ○ ○ ● ┌───┘
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    └───────┘

Step 17:
    ┌───────┐
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┌───┘ ○ ○ ● └───┐
│ ● ● ● ○ ● ○ ○ │
│ ○ ○ ● ● ● ○ ○ │
│ ○ ● ● ○ ● ● ○ │
└───┐ ○ ○ ○ ┌───┘
    │ ● ● ○ │
    └───────┘

Step 18:
    ┌───────┐
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┌───┘ ○ ○ ● └───┐
│ ● ● ● ○ ● ○ ○ │
│ ○ ○ ● ○ ○ ● ○ │
│ ○ ● ● ○ ● ● ○ │
└───┐ ○ ○ ○ ┌───┘
    │ ● ● ○ │
    └───────┘

Step 19:
    ┌───────┐
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┌───┘ ○ ○ ● └───┐
│ ● ● ● ○ ● ○ ○ │
│ ○ ○ ● ○ ○ ● ○ │
│ ○ ● ● ● ○ ○ ○ │
└───┐ ○ ○ ○ ┌───┘
    │ ● ● ○ │
    └───────┘

Step 20:
    ┌───────┐
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┌───┘ ○ ○ ● └───┐
│ ● ○ ○ ● ● ○ ○ │
│ ○ ○ ● ○ ○ ● ○ │
│ ○ ● ● ● ○ ○ ○ │
└───┐ ○ ○ ○ ┌───┘
    │ ● ● ○ │
    └───────┘

Step 21:
    ┌───────┐
    │ ○ ● ○ │
┌───┘ ○ ○ ● └───┐
│ ● ○ ○ ● ● ○ ○ │
│ ○ ○ ○ ○ ○ ● ○ │
│ ○ ● ○ ● ○ ○ ○ │
└───┐ ● ○ ○ ┌───┘
    │ ● ● ○ │
    └───────┘

Step 22:
    ┌───────┐
    │ ○ ● ○ │
┌───┘ ○ ○ ● └───┐
│ ● ○ ○ ● ● ○ ○ │
│ ○ ○ ○ ○ ○ ● ○ │
│ ○ ● ○ ● ○ ○ ○ │
└───┐ ● ○ ○ ┌───┘
    │ ○ ○ ● │
    └───────┘

Step 23:
    ┌───────┐
    │ ○ ● ○ │
┌───┘ ○ ○ ● └───┐
│ ● ○ ● ○ ○ ○ ○ │
│ ○ ○ ○ ○ ○ ● ○ │
│ ○ ● ○ ● ○ ○ ○ │
└───┐ ● ○ ○ ┌───┘
    │ ○ ○ ● │
    └───────┘

Solutions with 26 marbles left

Solution 0 with 3 ways to solve

Solutions with 22 marbles left

Solution 0 with 35 ways to solve

Solutions with 21 marbles left

Solution 0 with 900 ways to solve

Solutions with 19 marbles left

Solution 0 with 145 ways to solve
Solution 1 with 6 ways to solve
Solution 2 with 2423 ways to solve
Solution 3 with 1882 ways to solve
Solution 4 with 12313 ways to solve

Solutions with 18 marbles left

Solution 0 with 5217 ways to solve
Solution 1 with 3888 ways to solve
Solution 2 with 480 ways to solve
Solution 3 with 5856 ways to solve
Solution 4 with 24482 ways to solve
Solution 5 with 17188 ways to solve
Solution 6 with 1090 ways to solve
Solution 7 with 3179 ways to solve
Solution 8 with 2277 ways to solve
Solution 9 with 4396 ways to solve

Solutions with 17 marbles left

Solution 0 with 4414 ways to solve
Solution 1 with 7186 ways to solve
Solution 2 with 2994 ways to solve
Solution 3 with 6318 ways to solve
Solution 4 with 4737 ways to solve
Solution 5 with 35596 ways to solve
Solution 6 with 203106 ways to solve

Solutions with 16 marbles left

Solution 0 with 5487 ways to solve
Solution 1 with 47502 ways to solve
Solution 2 with 66952 ways to solve
Solution 3 with 280554 ways to solve
Solution 4 with 73891 ways to solve
Solution 5 with 3817 ways to solve
Solution 6 with 1732 ways to solve
Solution 7 with 308 ways to solve
Solution 8 with 2993 ways to solve
Solution 9 with 307232 ways to solve
Solution 10 with 51300 ways to solve
Solution 11 with 112563 ways to solve
Solution 12 with 37649 ways to solve
Solution 13 with 149134 ways to solve
Solution 14 with 19500 ways to solve
Solution 15 with 165148 ways to solve
Solution 16 with 607614 ways to solve
Solution 17 with 8683 ways to solve
Solution 18 with 968893 ways to solve
Solution 19 with 4266 ways to solve

Solutions with 15 marbles left

Solution 0 with 161113 ways to solve
Solution 1 with 15222 ways to solve
Solution 2 with 34380 ways to solve
Solution 3 with 41880 ways to solve
Solution 4 with 3701354 ways to solve
Solution 5 with 257173 ways to solve
Solution 6 with 34084 ways to solve
Solution 7 with 15413 ways to solve
Solution 8 with 6405 ways to solve
Solution 9 with 36 ways to solve
Solution 10 with 70209 ways to solve
Solution 11 with 15847 ways to solve
Solution 12 with 1712311 ways to solve
Solution 13 with 3087002 ways to solve
Solution 14 with 425 ways to solve
Solution 15 with 75774 ways to solve
Solution 16 with 40 ways to solve
Solution 17 with 311830 ways to solve
Solution 18 with 134341 ways to solve
Solution 19 with 14982 ways to solve

Solutions with 14 marbles left

Solution 0 with 166637 ways to solve
Solution 1 with 13473 ways to solve
Solution 2 with 68224 ways to solve
Solution 3 with 3744 ways to solve
Solution 4 with 509032 ways to solve
Solution 5 with 59375 ways to solve
Solution 6 with 121466 ways to solve
Solution 7 with 967629 ways to solve
Solution 8 with 22284 ways to solve
Solution 9 with 167419 ways to solve
Solution 10 with 4499 ways to solve
Solution 11 with 2854153 ways to solve
Solution 12 with 1116 ways to solve
Solution 13 with 121421 ways to solve
Solution 14 with 212856 ways to solve
Solution 15 with 1392512 ways to solve
Solution 16 with 3106313 ways to solve
Solution 17 with 91323 ways to solve
Solution 18 with 2311 ways to solve
Solution 19 with 1408753 ways to solve

Solutions with 13 marbles left

Solution 0 with 18202 ways to solve
Solution 1 with 9531216 ways to solve
Solution 2 with 6456632 ways to solve
Solution 3 with 1358695 ways to solve
Solution 4 with 11307601 ways to solve
Solution 5 with 61 ways to solve
Solution 6 with 4075980 ways to solve
Solution 7 with 131686 ways to solve
Solution 8 with 80967 ways to solve
Solution 9 with 1728354 ways to solve
Solution 10 with 1346514 ways to solve
Solution 11 with 3405150 ways to solve
Solution 12 with 95911 ways to solve
Solution 13 with 3315878 ways to solve
Solution 14 with 438831 ways to solve
Solution 15 with 2163702 ways to solve
Solution 16 with 857 ways to solve
Solution 17 with 49846 ways to solve
Solution 18 with 423352 ways to solve
Solution 19 with 4084793 ways to solve

Solutions with 12 marbles left

Solution 0 with 947319 ways to solve
Solution 1 with 5934872 ways to solve
Solution 2 with 543756 ways to solve
Solution 3 with 410059 ways to solve
Solution 4 with 29968596 ways to solve
Solution 5 with 4864781 ways to solve
Solution 6 with 908 ways to solve
Solution 7 with 2554796 ways to solve
Solution 8 with 225854984 ways to solve
Solution 9 with 17873228 ways to solve
Solution 10 with 14623359 ways to solve
Solution 11 with 2258893 ways to solve
Solution 12 with 23290633 ways to solve
Solution 13 with 19833862 ways to solve
Solution 14 with 976839 ways to solve
Solution 15 with 6256641 ways to solve
Solution 16 with 60173386 ways to solve
Solution 17 with 5357023 ways to solve
Solution 18 with 99558 ways to solve
Solution 19 with 13242 ways to solve

Solutions with 11 marbles left

Solution 0 with 20790028 ways to solve
Solution 1 with 41705312 ways to solve
Solution 2 with 2880487 ways to solve
Solution 3 with 1215861 ways to solve
Solution 4 with 164521815 ways to solve
Solution 5 with 1416816 ways to solve
Solution 6 with 861840 ways to solve
Solution 7 with 35741470 ways to solve
Solution 8 with 38631451 ways to solve
Solution 9 with 1472616 ways to solve
Solution 10 with 21911346 ways to solve
Solution 11 with 132234632 ways to solve
Solution 12 with 9471752 ways to solve
Solution 13 with 121558 ways to solve
Solution 14 with 14627910 ways to solve
Solution 15 with 35688078 ways to solve
Solution 16 with 41592237 ways to solve
Solution 17 with 78826568 ways to solve
Solution 18 with 90232469 ways to solve
Solution 19 with 185503717 ways to solve

Solutions with 10 marbles left

Solution 0 with 83469921 ways to solve
Solution 1 with 43887322 ways to solve
Solution 2 with 42199144 ways to solve
Solution 3 with 2230997906 ways to solve
Solution 4 with 176220298 ways to solve
Solution 5 with 1771245423 ways to solve
Solution 6 with 2403519 ways to solve
Solution 7 with 125778869 ways to solve
Solution 8 with 854122505 ways to solve
Solution 9 with 411633200 ways to solve
Solution 10 with 309120642 ways to solve
Solution 11 with 641007 ways to solve
Solution 12 with 2087898628 ways to solve
Solution 13 with 508352673 ways to solve
Solution 14 with 132499470 ways to solve
Solution 15 with 38448516 ways to solve
Solution 16 with 400033339 ways to solve
Solution 17 with 408485474 ways to solve
Solution 18 with 54166759 ways to solve
Solution 19 with 3093636 ways to solve

Solutions with 9 marbles left

Solution 0 with 28239147279 ways to solve
Solution 1 with 913930787 ways to solve
Solution 2 with 1706342199 ways to solve
Solution 3 with 3058357873 ways to solve
Solution 4 with 37222039 ways to solve
Solution 5 with 155112207 ways to solve
Solution 6 with 8298930864 ways to solve
Solution 7 with 4966274 ways to solve
Solution 8 with 588567696 ways to solve
Solution 9 with 932839696 ways to solve
Solution 10 with 13177252265 ways to solve
Solution 11 with 5006220921 ways to solve
Solution 12 with 470142979 ways to solve
Solution 13 with 782120157 ways to solve
Solution 14 with 420679718 ways to solve
Solution 15 with 307746068 ways to solve
Solution 16 with 1114654770 ways to solve
Solution 17 with 8590151388 ways to solve
Solution 18 with 18777661856 ways to solve
Solution 19 with 98756998 ways to solve

Solutions with 8 marbles left

Solution 0 with 9994704883 ways to solve
Solution 1 with 3240952952 ways to solve
Solution 2 with 46095687660 ways to solve
Solution 3 with 2051530694 ways to solve
Solution 4 with 2927004907 ways to solve
Solution 5 with 309462453 ways to solve
Solution 6 with 8418887589 ways to solve
Solution 7 with 6509655380 ways to solve
Solution 8 with 4317194503 ways to solve
Solution 9 with 5350545067 ways to solve
Solution 10 with 1538643195 ways to solve
Solution 11 with 38088830634 ways to solve
Solution 12 with 267851666 ways to solve
Solution 13 with 7813063298 ways to solve
Solution 14 with 3324610090 ways to solve
Solution 15 with 2093491551 ways to solve
Solution 16 with 14855240167 ways to solve
Solution 17 with 5987924127 ways to solve
Solution 18 with 10934703271 ways to solve
Solution 19 with 32434867 ways to solve

Solutions with 7 marbles left

Solution 0 with 437801698 ways to solve
Solution 1 with 10569125322 ways to solve
Solution 2 with 12274551776 ways to solve
Solution 3 with 77548007305 ways to solve
Solution 4 with 13287939419 ways to solve
Solution 5 with 95753833968 ways to solve
Solution 6 with 18718866542 ways to solve
Solution 7 with 7080233482 ways to solve
Solution 8 with 12212394305 ways to solve
Solution 9 with 28651385924 ways to solve
Solution 10 with 2412408261 ways to solve
Solution 11 with 18401849793 ways to solve
Solution 12 with 1373226020 ways to solve
Solution 13 with 66653326875 ways to solve
Solution 14 with 28023461214 ways to solve
Solution 15 with 1040467728 ways to solve
Solution 16 with 85814140017 ways to solve
Solution 17 with 237952568 ways to solve
Solution 18 with 16021510076 ways to solve
Solution 19 with 149182 ways to solve

Solutions with 6 marbles left

Solution 0 with 180642010555 ways to solve
Solution 1 with 253020980554 ways to solve
Solution 2 with 21175182743 ways to solve
Solution 3 with 37824274523 ways to solve
Solution 4 with 141622827975 ways to solve
Solution 5 with 2176730718 ways to solve
Solution 6 with 46508148553 ways to solve
Solution 7 with 82933872950 ways to solve
Solution 8 with 99642797139 ways to solve
Solution 9 with 571516351489 ways to solve
Solution 10 with 26799423309 ways to solve
Solution 11 with 10942680411 ways to solve
Solution 12 with 29317389772 ways to solve
Solution 13 with 5892025620 ways to solve
Solution 14 with 146164189873 ways to solve
Solution 15 with 9240690168 ways to solve
Solution 16 with 258276732392 ways to solve
Solution 17 with 76539386735 ways to solve
Solution 18 with 11416982048 ways to solve
Solution 19 with 98450682991 ways to solve

Solutions with 5 marbles left

Solution 0 with 1128517871940 ways to solve
Solution 1 with 187169539907 ways to solve
Solution 2 with 70501019411 ways to solve
Solution 3 with 365830678778 ways to solve
Solution 4 with 7720512712 ways to solve
Solution 5 with 170916133208 ways to solve
Solution 6 with 12487628509 ways to solve
Solution 7 with 2728111387248 ways to solve
Solution 8 with 3873011012 ways to solve
Solution 9 with 450720779711 ways to solve
Solution 10 with 17011240672 ways to solve
Solution 11 with 797746643886 ways to solve
Solution 12 with 501213622861 ways to solve
Solution 13 with 18918622662 ways to solve
Solution 14 with 823689683126 ways to solve
Solution 15 with 131842837677 ways to solve
Solution 16 with 1182484910214 ways to solve
Solution 17 with 358080621200 ways to solve
Solution 18 with 77761757771 ways to solve
Solution 19 with 1737158333710 ways to solve

Solutions with 4 marbles left

Solution 0 with 877808100036 ways to solve
Solution 1 with 8248238624 ways to solve
Solution 2 with 295519702354 ways to solve
Solution 3 with 3175987313382 ways to solve
Solution 4 with 9612213568 ways to solve
Solution 5 with 485023589389 ways to solve
Solution 6 with 2759971037 ways to solve
Solution 7 with 16500713381 ways to solve
Solution 8 with 305032552420 ways to solve
Solution 9 with 342456065153 ways to solve
Solution 10 with 520031278269 ways to solve
Solution 11 with 1018785765 ways to solve
Solution 12 with 9225286499 ways to solve
Solution 13 with 131974755 ways to solve
Solution 14 with 106373478165 ways to solve
Solution 15 with 914477529322 ways to solve
Solution 16 with 1540234208087 ways to solve
Solution 17 with 178427428139 ways to solve
Solution 18 with 323138927529 ways to solve
Solution 19 with 4575344238 ways to solve

Solutions with 3 marbles left

Solution 0 with 20854188 ways to solve
Solution 1 with 3520974020274 ways to solve
Solution 2 with 291119566311 ways to solve
Solution 3 with 462809306715 ways to solve
Solution 4 with 275255054593 ways to solve
Solution 5 with 1246818914202 ways to solve
Solution 6 with 59868555497 ways to solve
Solution 7 with 346418788213 ways to solve
Solution 8 with 4863511335887 ways to solve
Solution 9 with 3430250562 ways to solve
Solution 10 with 1374807757977 ways to solve
Solution 11 with 308754314088 ways to solve
Solution 12 with 1149926992695 ways to solve
Solution 13 with 951768650972 ways to solve
Solution 14 with 1337354793108 ways to solve
Solution 15 with 255105345265 ways to solve
Solution 16 with 1080074825282 ways to solve
Solution 17 with 5749338012 ways to solve
Solution 18 with 474672046961 ways to solve
Solution 19 with 2412197226719 ways to solve

Solutions with 2 marbles left

Solution 0 with 5054584780 ways to solve
Solution 1 with 32519810378 ways to solve
Solution 2 with 248137702973 ways to solve
Solution 3 with 417340974290 ways to solve
Solution 4 with 397584289435 ways to solve
Solution 5 with 19755233098 ways to solve

Solutions with 1 marbles left

Solution 0 with 1713819723445 ways to solve
Solution 1 with 1713819723445 ways to solve

solution_9_6

Solution 6

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