{
  "id": 567621,
  "title": "Number of ways to fold",
  "url": "/competitions/stanford-rna-3d-folding/discussion/567621",
  "author_name": "Ekalabya Ghosh",
  "post_date": "2025-03-11T06:51:06.241000",
  "votes": 3,
  "comment_count": 0,
  "views": 0,
  "content": "<p>This is the exact number of ways, an RNA chain of length 5000 ( which is close to the longest chain in the data set ) can fold - <br>\n19,950,631,168,807,583,848,837,421,626,835,850,838,234,968,318,861,924,548,520,089,498,529,438,830,221,946,631,919,961,684,036,194,597,899,331,129,423,209,124,271,556,491,349,413,781,117,593,785,932,096,323,957,855,730,046,793,794,526,765,246,551,266,059,895,520,550,086,918,193,311,542,508,608,460,618,104,685,509,074,866,089,624,888,090,489,894,838,009,253,941,633,257,850,621,568,309,473,902,556,912,388,065,225,096,643,874,441,046,759,871,626,985,453,222,868,538,161,694,315,775,629,640,762,836,880,760,732,228,535,091,641,476,183,956,381,458,969,463,899,410,840,960,536,267,821,064,621,427,333,394,036,525,565,649,530,603,142,680,234,969,400,335,934,316,651,459,297,773,279,665,775,606,172,582,031,407,994,198,179,607,378,245,683,762,280,037,302,885,487,251,900,834,464,581,454,650,557,929,601,414,833,921,615,734,588,139,257,095,379,769,119,277,800,826,957,735,674,444,123,062,018,757,836,325,502,728,323,789,270,710,373,802,866,393,031,428,133,241,401,624,195,671,690,574,061,419,654,342,324,638,801,248,856,147,305,207,431,992,259,611,796,250,130,992,860,241,708,340,807,605,932,320,161,268,492,288,496,255,841,312,844,061,536,738,951,487,114,256,315,111,089,745,514,203,313,820,202,931,640,957,596,464,756,010,405,845,841,566,072,044,962,867,016,515,061,920,631,004,186,422,275,908,670,900,574,606,417,856,951,911,456,055,068,251,250,406,007,519,842,261,898,059,237,118,054,444,788,072,906,395,242,548,339,221,982,707,404,473,162,376,760,846,613,033,778,706,039,803,413,197,133,493,654,622,700,563,169,937,455,508,241,780,972,810,983,291,314,403,571,877,524,768,509,857,276,937,926,433,221,599,399,876,886,660,808,368,837,838,027,643,282,775,172,273,657,572,744,784,112,294,389,733,810,861,607,423,253,291,974,813,120,197,604,178,281,965,697,475,898,164,531,258,434,135,959,862,784,130,128,185,406,283,476,649,088,690,521,047,580,882,615,823,961,985,770,122,407,044,330,583,075,869,039,319,604,603,404,973,156,583,208,672,105,913,300,903,752,823,415,539,745,394,397,715,257,455,290,510,212,310,947,321,610,753,474,825,740,775,273,986,348,298,498,340,756,937,955,646,638,621,874,569,499,279,016,572,103,701,364,433,135,817,214,311,791,398,222,983,845,847,334,440,270,964,182,851,005,072,927,748,364,550,578,634,501,100,852,987,812,389,473,928,699,540,834,346,158,807,043,959,118,985,815,145,779,177,143,619,698,728,131,459,483,783,202,081,474,982,171,858,011,389,071,228,250,905,826,817,436,220,577,475,921,417,653,715,687,725,614,904,582,904,992,461,028,630,081,535,583,308,130,101,987,675,856,234,343,538,955,409,175,623,400,844,887,526,162,643,568,648,833,519,463,720,377,293,240,094,456,246,923,254,350,400,678,027,273,837,755,376,406,726,898,636,241,037,491,410,966,718,557,050,759,098,100,246,789,880,178,271,925,953,381,282,421,954,028,302,759,408,448,955,014,676,668,389,697,996,886,241,636,313,376,393,903,373,455,801,407,636,741,877,711,055,384,225,739,499,110,186,468,219,696,581,651,485,130,494,222,369,947,714,763,069,155,468,217,682,876,200,362,777,257,723,781,365,331,611,196,811,280,792,669,481,887,201,298,643,660,768,551,639,860,534,602,297,871,557,517,947,385,246,369,446,923,087,894,265,948,217,008,051,120,322,365,496,288,169,035,739,121,368,338,393,591,756,418,733,850,510,970,271,613,915,439,590,991,598,154,654,417,336,311,656,936,031,122,249,937,969,999,226,781,732,358,023,111,862,644,575,299,135,758,175,008,199,839,236,284,615,249,881,088,960,232,244,362,173,771,618,086,357,015,468,484,058,622,329,792,853,875,623,486,556,440,536,962,622,018,963,571,028,812,361,567,512,543,338,303,270,029,097,668,650,568,557,157,505,516,727,518,899,194,129,711,337,690,149,916,181,315,171,544,007,728,650,573,189,557,450,920,330,185,304,847,113,818,315,407,324,053,319,038,462,084,036,421,763,703,911,550,639,789,000,742,853,672,196,280,903,477,974,533,320,468,368,795,868,580,237,952,218,629,120,080,742,819,551,317,948,157,624,448,298,518,461,509,704,888,027,274,721,574,688,131,594,750,409,732,115,080,498,190,455,803,416,826,949,787,141,316,063,210,686,391,511,681,774,304,792,596,709,376</p>",
  "messages": [
    {
      "id": 3146696,
      "postDate": "2025-03-11T06:51:06.240Z",
      "content": "<p>This is the exact number of ways, an RNA chain of length 5000 ( which is close to the longest chain in the data set ) can fold - <br>\n19,950,631,168,807,583,848,837,421,626,835,850,838,234,968,318,861,924,548,520,089,498,529,438,830,221,946,631,919,961,684,036,194,597,899,331,129,423,209,124,271,556,491,349,413,781,117,593,785,932,096,323,957,855,730,046,793,794,526,765,246,551,266,059,895,520,550,086,918,193,311,542,508,608,460,618,104,685,509,074,866,089,624,888,090,489,894,838,009,253,941,633,257,850,621,568,309,473,902,556,912,388,065,225,096,643,874,441,046,759,871,626,985,453,222,868,538,161,694,315,775,629,640,762,836,880,760,732,228,535,091,641,476,183,956,381,458,969,463,899,410,840,960,536,267,821,064,621,427,333,394,036,525,565,649,530,603,142,680,234,969,400,335,934,316,651,459,297,773,279,665,775,606,172,582,031,407,994,198,179,607,378,245,683,762,280,037,302,885,487,251,900,834,464,581,454,650,557,929,601,414,833,921,615,734,588,139,257,095,379,769,119,277,800,826,957,735,674,444,123,062,018,757,836,325,502,728,323,789,270,710,373,802,866,393,031,428,133,241,401,624,195,671,690,574,061,419,654,342,324,638,801,248,856,147,305,207,431,992,259,611,796,250,130,992,860,241,708,340,807,605,932,320,161,268,492,288,496,255,841,312,844,061,536,738,951,487,114,256,315,111,089,745,514,203,313,820,202,931,640,957,596,464,756,010,405,845,841,566,072,044,962,867,016,515,061,920,631,004,186,422,275,908,670,900,574,606,417,856,951,911,456,055,068,251,250,406,007,519,842,261,898,059,237,118,054,444,788,072,906,395,242,548,339,221,982,707,404,473,162,376,760,846,613,033,778,706,039,803,413,197,133,493,654,622,700,563,169,937,455,508,241,780,972,810,983,291,314,403,571,877,524,768,509,857,276,937,926,433,221,599,399,876,886,660,808,368,837,838,027,643,282,775,172,273,657,572,744,784,112,294,389,733,810,861,607,423,253,291,974,813,120,197,604,178,281,965,697,475,898,164,531,258,434,135,959,862,784,130,128,185,406,283,476,649,088,690,521,047,580,882,615,823,961,985,770,122,407,044,330,583,075,869,039,319,604,603,404,973,156,583,208,672,105,913,300,903,752,823,415,539,745,394,397,715,257,455,290,510,212,310,947,321,610,753,474,825,740,775,273,986,348,298,498,340,756,937,955,646,638,621,874,569,499,279,016,572,103,701,364,433,135,817,214,311,791,398,222,983,845,847,334,440,270,964,182,851,005,072,927,748,364,550,578,634,501,100,852,987,812,389,473,928,699,540,834,346,158,807,043,959,118,985,815,145,779,177,143,619,698,728,131,459,483,783,202,081,474,982,171,858,011,389,071,228,250,905,826,817,436,220,577,475,921,417,653,715,687,725,614,904,582,904,992,461,028,630,081,535,583,308,130,101,987,675,856,234,343,538,955,409,175,623,400,844,887,526,162,643,568,648,833,519,463,720,377,293,240,094,456,246,923,254,350,400,678,027,273,837,755,376,406,726,898,636,241,037,491,410,966,718,557,050,759,098,100,246,789,880,178,271,925,953,381,282,421,954,028,302,759,408,448,955,014,676,668,389,697,996,886,241,636,313,376,393,903,373,455,801,407,636,741,877,711,055,384,225,739,499,110,186,468,219,696,581,651,485,130,494,222,369,947,714,763,069,155,468,217,682,876,200,362,777,257,723,781,365,331,611,196,811,280,792,669,481,887,201,298,643,660,768,551,639,860,534,602,297,871,557,517,947,385,246,369,446,923,087,894,265,948,217,008,051,120,322,365,496,288,169,035,739,121,368,338,393,591,756,418,733,850,510,970,271,613,915,439,590,991,598,154,654,417,336,311,656,936,031,122,249,937,969,999,226,781,732,358,023,111,862,644,575,299,135,758,175,008,199,839,236,284,615,249,881,088,960,232,244,362,173,771,618,086,357,015,468,484,058,622,329,792,853,875,623,486,556,440,536,962,622,018,963,571,028,812,361,567,512,543,338,303,270,029,097,668,650,568,557,157,505,516,727,518,899,194,129,711,337,690,149,916,181,315,171,544,007,728,650,573,189,557,450,920,330,185,304,847,113,818,315,407,324,053,319,038,462,084,036,421,763,703,911,550,639,789,000,742,853,672,196,280,903,477,974,533,320,468,368,795,868,580,237,952,218,629,120,080,742,819,551,317,948,157,624,448,298,518,461,509,704,888,027,274,721,574,688,131,594,750,409,732,115,080,498,190,455,803,416,826,949,787,141,316,063,210,686,391,511,681,774,304,792,596,709,376</p>",
      "rawMarkdown": "This is the exact number of ways, an RNA chain of length 5000 ( which is close to the longest chain in the data set ) can fold - \n19,950,631,168,807,583,848,837,421,626,835,850,838,234,968,318,861,924,548,520,089,498,529,438,830,221,946,631,919,961,684,036,194,597,899,331,129,423,209,124,271,556,491,349,413,781,117,593,785,932,096,323,957,855,730,046,793,794,526,765,246,551,266,059,895,520,550,086,918,193,311,542,508,608,460,618,104,685,509,074,866,089,624,888,090,489,894,838,009,253,941,633,257,850,621,568,309,473,902,556,912,388,065,225,096,643,874,441,046,759,871,626,985,453,222,868,538,161,694,315,775,629,640,762,836,880,760,732,228,535,091,641,476,183,956,381,458,969,463,899,410,840,960,536,267,821,064,621,427,333,394,036,525,565,649,530,603,142,680,234,969,400,335,934,316,651,459,297,773,279,665,775,606,172,582,031,407,994,198,179,607,378,245,683,762,280,037,302,885,487,251,900,834,464,581,454,650,557,929,601,414,833,921,615,734,588,139,257,095,379,769,119,277,800,826,957,735,674,444,123,062,018,757,836,325,502,728,323,789,270,710,373,802,866,393,031,428,133,241,401,624,195,671,690,574,061,419,654,342,324,638,801,248,856,147,305,207,431,992,259,611,796,250,130,992,860,241,708,340,807,605,932,320,161,268,492,288,496,255,841,312,844,061,536,738,951,487,114,256,315,111,089,745,514,203,313,820,202,931,640,957,596,464,756,010,405,845,841,566,072,044,962,867,016,515,061,920,631,004,186,422,275,908,670,900,574,606,417,856,951,911,456,055,068,251,250,406,007,519,842,261,898,059,237,118,054,444,788,072,906,395,242,548,339,221,982,707,404,473,162,376,760,846,613,033,778,706,039,803,413,197,133,493,654,622,700,563,169,937,455,508,241,780,972,810,983,291,314,403,571,877,524,768,509,857,276,937,926,433,221,599,399,876,886,660,808,368,837,838,027,643,282,775,172,273,657,572,744,784,112,294,389,733,810,861,607,423,253,291,974,813,120,197,604,178,281,965,697,475,898,164,531,258,434,135,959,862,784,130,128,185,406,283,476,649,088,690,521,047,580,882,615,823,961,985,770,122,407,044,330,583,075,869,039,319,604,603,404,973,156,583,208,672,105,913,300,903,752,823,415,539,745,394,397,715,257,455,290,510,212,310,947,321,610,753,474,825,740,775,273,986,348,298,498,340,756,937,955,646,638,621,874,569,499,279,016,572,103,701,364,433,135,817,214,311,791,398,222,983,845,847,334,440,270,964,182,851,005,072,927,748,364,550,578,634,501,100,852,987,812,389,473,928,699,540,834,346,158,807,043,959,118,985,815,145,779,177,143,619,698,728,131,459,483,783,202,081,474,982,171,858,011,389,071,228,250,905,826,817,436,220,577,475,921,417,653,715,687,725,614,904,582,904,992,461,028,630,081,535,583,308,130,101,987,675,856,234,343,538,955,409,175,623,400,844,887,526,162,643,568,648,833,519,463,720,377,293,240,094,456,246,923,254,350,400,678,027,273,837,755,376,406,726,898,636,241,037,491,410,966,718,557,050,759,098,100,246,789,880,178,271,925,953,381,282,421,954,028,302,759,408,448,955,014,676,668,389,697,996,886,241,636,313,376,393,903,373,455,801,407,636,741,877,711,055,384,225,739,499,110,186,468,219,696,581,651,485,130,494,222,369,947,714,763,069,155,468,217,682,876,200,362,777,257,723,781,365,331,611,196,811,280,792,669,481,887,201,298,643,660,768,551,639,860,534,602,297,871,557,517,947,385,246,369,446,923,087,894,265,948,217,008,051,120,322,365,496,288,169,035,739,121,368,338,393,591,756,418,733,850,510,970,271,613,915,439,590,991,598,154,654,417,336,311,656,936,031,122,249,937,969,999,226,781,732,358,023,111,862,644,575,299,135,758,175,008,199,839,236,284,615,249,881,088,960,232,244,362,173,771,618,086,357,015,468,484,058,622,329,792,853,875,623,486,556,440,536,962,622,018,963,571,028,812,361,567,512,543,338,303,270,029,097,668,650,568,557,157,505,516,727,518,899,194,129,711,337,690,149,916,181,315,171,544,007,728,650,573,189,557,450,920,330,185,304,847,113,818,315,407,324,053,319,038,462,084,036,421,763,703,911,550,639,789,000,742,853,672,196,280,903,477,974,533,320,468,368,795,868,580,237,952,218,629,120,080,742,819,551,317,948,157,624,448,298,518,461,509,704,888,027,274,721,574,688,131,594,750,409,732,115,080,498,190,455,803,416,826,949,787,141,316,063,210,686,391,511,681,774,304,792,596,709,376",
      "votes": 3
    }
  ],
  "comments": [],
  "raw_markdown_by_id": {
    "3146696": "This is the exact number of ways, an RNA chain of length 5000 ( which is close to the longest chain in the data set ) can fold - \n19,950,631,168,807,583,848,837,421,626,835,850,838,234,968,318,861,924,548,520,089,498,529,438,830,221,946,631,919,961,684,036,194,597,899,331,129,423,209,124,271,556,491,349,413,781,117,593,785,932,096,323,957,855,730,046,793,794,526,765,246,551,266,059,895,520,550,086,918,193,311,542,508,608,460,618,104,685,509,074,866,089,624,888,090,489,894,838,009,253,941,633,257,850,621,568,309,473,902,556,912,388,065,225,096,643,874,441,046,759,871,626,985,453,222,868,538,161,694,315,775,629,640,762,836,880,760,732,228,535,091,641,476,183,956,381,458,969,463,899,410,840,960,536,267,821,064,621,427,333,394,036,525,565,649,530,603,142,680,234,969,400,335,934,316,651,459,297,773,279,665,775,606,172,582,031,407,994,198,179,607,378,245,683,762,280,037,302,885,487,251,900,834,464,581,454,650,557,929,601,414,833,921,615,734,588,139,257,095,379,769,119,277,800,826,957,735,674,444,123,062,018,757,836,325,502,728,323,789,270,710,373,802,866,393,031,428,133,241,401,624,195,671,690,574,061,419,654,342,324,638,801,248,856,147,305,207,431,992,259,611,796,250,130,992,860,241,708,340,807,605,932,320,161,268,492,288,496,255,841,312,844,061,536,738,951,487,114,256,315,111,089,745,514,203,313,820,202,931,640,957,596,464,756,010,405,845,841,566,072,044,962,867,016,515,061,920,631,004,186,422,275,908,670,900,574,606,417,856,951,911,456,055,068,251,250,406,007,519,842,261,898,059,237,118,054,444,788,072,906,395,242,548,339,221,982,707,404,473,162,376,760,846,613,033,778,706,039,803,413,197,133,493,654,622,700,563,169,937,455,508,241,780,972,810,983,291,314,403,571,877,524,768,509,857,276,937,926,433,221,599,399,876,886,660,808,368,837,838,027,643,282,775,172,273,657,572,744,784,112,294,389,733,810,861,607,423,253,291,974,813,120,197,604,178,281,965,697,475,898,164,531,258,434,135,959,862,784,130,128,185,406,283,476,649,088,690,521,047,580,882,615,823,961,985,770,122,407,044,330,583,075,869,039,319,604,603,404,973,156,583,208,672,105,913,300,903,752,823,415,539,745,394,397,715,257,455,290,510,212,310,947,321,610,753,474,825,740,775,273,986,348,298,498,340,756,937,955,646,638,621,874,569,499,279,016,572,103,701,364,433,135,817,214,311,791,398,222,983,845,847,334,440,270,964,182,851,005,072,927,748,364,550,578,634,501,100,852,987,812,389,473,928,699,540,834,346,158,807,043,959,118,985,815,145,779,177,143,619,698,728,131,459,483,783,202,081,474,982,171,858,011,389,071,228,250,905,826,817,436,220,577,475,921,417,653,715,687,725,614,904,582,904,992,461,028,630,081,535,583,308,130,101,987,675,856,234,343,538,955,409,175,623,400,844,887,526,162,643,568,648,833,519,463,720,377,293,240,094,456,246,923,254,350,400,678,027,273,837,755,376,406,726,898,636,241,037,491,410,966,718,557,050,759,098,100,246,789,880,178,271,925,953,381,282,421,954,028,302,759,408,448,955,014,676,668,389,697,996,886,241,636,313,376,393,903,373,455,801,407,636,741,877,711,055,384,225,739,499,110,186,468,219,696,581,651,485,130,494,222,369,947,714,763,069,155,468,217,682,876,200,362,777,257,723,781,365,331,611,196,811,280,792,669,481,887,201,298,643,660,768,551,639,860,534,602,297,871,557,517,947,385,246,369,446,923,087,894,265,948,217,008,051,120,322,365,496,288,169,035,739,121,368,338,393,591,756,418,733,850,510,970,271,613,915,439,590,991,598,154,654,417,336,311,656,936,031,122,249,937,969,999,226,781,732,358,023,111,862,644,575,299,135,758,175,008,199,839,236,284,615,249,881,088,960,232,244,362,173,771,618,086,357,015,468,484,058,622,329,792,853,875,623,486,556,440,536,962,622,018,963,571,028,812,361,567,512,543,338,303,270,029,097,668,650,568,557,157,505,516,727,518,899,194,129,711,337,690,149,916,181,315,171,544,007,728,650,573,189,557,450,920,330,185,304,847,113,818,315,407,324,053,319,038,462,084,036,421,763,703,911,550,639,789,000,742,853,672,196,280,903,477,974,533,320,468,368,795,868,580,237,952,218,629,120,080,742,819,551,317,948,157,624,448,298,518,461,509,704,888,027,274,721,574,688,131,594,750,409,732,115,080,498,190,455,803,416,826,949,787,141,316,063,210,686,391,511,681,774,304,792,596,709,376"
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