Statistics

Problem Statement for "NumberGrid"

Problem Statement

NOTE: This problem statement contains subscripts that may not display properly if viewed outside of the applet.


A number grid is a rectangular matrix where each cell is a digit between 0 and 9, inclusive.

Given a number grid G, an encrypted grid E with the same dimensions can be generated using the following procedure (using zero-based indexing):

for(i=0;i<rows;++i){
  for(j=0;j<cols;++j){
    Ei,j = 0
    for(r=0;r<rows;++r){
      for(c=0;c<cols;++c){
        if( (r equals i) or (c equals j))
        {Ei,j = Ei,j + Gr,c}
      }
    }
  }
}

Note that this means each cell in E is the sum of all the cells in G that positionally share the same row or column. (The cell in G with both the same row and same column is only counted once.)

An example number grid G is given below:

-------------
| 0 | 1 | 3 |
-------------
| 2 | 5 | 7 |
-------------
Performing the above procedure yields the encrypted grid below: 
----------------
| 6  | 9  | 11 |
----------------
| 14 | 15 | 17 |
----------------

The cell in row 0, column 1 of E, for example, is calculated by taking the sum of all cells in G with either row 0 or column 1 (0 + 1 + 3 + 5 = 9). Note that the '1' cell is counted only once.


Given an encrypted grid E, reconstruct the original number grid G if possible.


The encrypted grid is given in three separate String[]s. hundreds gives the digit in the hundreds place of each cell in the encrypted grid, tens gives the digit in the tens place, and ones gives the digit in the ones place. In each of these String[]s, the j-th character of the i-th element represents the cell in row i, column j.


For example, if the encrypted grid appeared as follows:

------------------
| 106 | 72  | 5  |
------------------
| 14  | 135 | 17 |
------------------

The input would appear like this:


hundreds 
{"100",
 "010"}

tens 
{"070",
 "131"}

ones 
{"625",
 "457"}

If there is exactly one valid number grid G that yields the given encrypted grid, return a String[] representing G, where the j-th character of the i-th element is the digit in row i, column j. If there are no possible number grids, return a String[] containing exactly one element: "NO SOLUTIONS" (quotes for clarity only). If there are multiple distinct solutions, return a String[] containing exactly one element, formatted as "n SOLUTIONS" (quotes for clarity only), where n is the number of solutions modulo 1000000007 (10^9 + 7), with no extra leading zeroes.

Definition

Class:
NumberGrid
Method:
decrypt
Parameters:
String[], String[], String[]
Returns:
String[]
Method signature:
String[] decrypt(String[] hundreds, String[] tens, String[] ones)
(be sure your method is public)

Notes

  • Two number grids G1 and G2 are considered distinct if at least one entry in G1 is different from the corresponding entry in G2.

Constraints

  • hundreds will contain between 1 and 50 elements, inclusive.
  • Each element of hundreds will contain between 1 and 50 characters, inclusive.
  • Each element of hundreds will have the same number of characters.
  • Each element of hundreds will contain only digits ('0' - '9').
  • tens and ones will have the same number of elements as hundreds.
  • Each element of tens and ones will have the same number of characters as each element of hundreds.
  • Each element of tens and ones will contain only digits ('0' - '9').

Examples

  1. {"000", "000"}

    {"001", "111"}

    {"691", "457"}

    Returns: {"013", "257" }

    The example given in the problem statement.

  2. {"0"}

    {"0"}

    {"3"}

    Returns: {"3" }

    A single cell means that the solution is equal to the input...

  3. {"0"}

    {"4"}

    {"2"}

    Returns: {"NO SOLUTIONS" }

    ...unless the input would not be a valid number grid.

  4. {"00000"}

    {"00000"}

    {"22222"}

    Returns: {"15 SOLUTIONS" }

    There many number grids that generate this encrypted grid, using either 1) one '2' and four '0' in any order => 5 ways 2) two '1' and three '0' in any order => 10 ways for a grand total of 15 solutions.

  5. {"0","0","0","0","0","0"}

    {"5","5","5","5","5","5"}

    {"4","4","4","4","4","4"}

    Returns: {"9", "9", "9", "9", "9", "9" }

  6. {"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000"}

    {"33333334443333333333333333333333334444333333344443", "33443334444433443344443443344443334444333444444443", "12222222232211221222222221122221112222222222222222", "11221112222211221112221221122221112222111212222221", "11221112222211221112221221122221112222111212222221", "11221112222211221112221221122221112222111212222221", "11221112222211221112221221122221112222111212222221", "22222223332222222222222222222222222233222222232332", "12222222232222222222222222222222222223222222222222", "00000001110000000000000000000000000011000000011110", "00000001110000000000000000000000000011000000011110", "22222223332222222223332332233222223333222223333332", "22222223332222222222222222222222222233222222233322", "12222222222211221122222221122221112222111222222221", "11111112221111111111111111111111112222111112122221", "12222222232222222222222222222222222222222222222222", "11111112221111111112221111122121112222111112222221", "22222223332222222222222222222222222233222222233322", "23333333343322332233333332233332223333333333333333", "00000001110000000000000000000000000011000000011110", "00000001110000000000000000000000000011000000011110", "00000001110000000000000000000000000011000000011110"}

    {"15665552256622663579996773388683330022444659811215", "59009996690066007913329117722017774356889103254559", "61221117702288228023331339944128884467000215465650", "49009995580066006891129117722016662245888093243438", "49009995580066006891129117722016662245888093243438", "49009995580066006891129117722016662245888093243438", "49009995580066006891129117722016662245888093143448", "05665551146622662467774773377562229801334658709104", "83443339924400440246652440055450007790111326598982", "05665552256622662468885773388672229912444659810104", "05665552256622662468885773388672229912444659810104", "38887774479955995680008006611994441245777981032337", "05665552245522651368874673387562228802444548810094", "50110007790077007913330118822127774456998004365648", "16776663356633673579996874489783330022554660921204", "83442229924400340246663541156450007799222426587871", "37888885589955885791118996600905552234777982143426", "04555552256622651368874673387562228802444548810094", "60110007701188228913331339944227774578000214365660", "05665552256622662468885773388672229912444659810104", "05665552256622662468885773388672229912444659810104", "05665552256622662468885773388672229912444659810104"}

    Returns: {"01111111111111110000000111111100000001111111110000", "01111111111111110000011111111110000111110001111100", "00000001110000000001110000000110001111000000011110", "00000001110000000011100000000000001111000000011110", "00000001110000000011100000000000001111000000011110", "00000001110000000011100000000000001111000000011110", "00000001110000000011100000000000001111000000111100", "00000001110000000001111000011110000111110001111000", "00000001110000000000011111111000000000111111100000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00111111110000000111110000000011111000000001111100", "00000000011100011100011100001110001110000111000110", "00000000011100110000000110011000000011001100000011", "00000000011100100000000010010000000001001100000011", "00001111110000100000000010010000000001000011111111", "01110000000000110000000110011000000011000000000011", "01110000000000011100011100001110001110000111000110", "01111111111100000111110000000011111000000001111100", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }

    the old TCO 2009 sample

  7. {"22222222222222222222222222222222222222222222222222"}

    {"55555555555555555555555555555555555555555555555555"}

    {"11111111111111111111111111111111111111111111111111"}

    Returns: {"106591981 SOLUTIONS" }

    A case with high enough solutions to use the modulus.

  8. {"0"}

    {"0"}

    {"7"}

    Returns: {"7" }

  9. {"34434443444434434444433444444443444444444444444444","34434443343434334444333444444443344444434444444443","44444444444444444444434444444444444444444444444444","45444444444444444444444444444444444454444444445444","44444444444444444444444444444444444444444444444444","44444444444444444444444444444444444444444444444444","34434443444434434444333444444443444444444444444444","44444444444444444444444444444444444444444444444444","45444444444444444444444444444444444454444444445444","44444444444444444444434444444444444444444444444444","34444443444444444444434444444444444444444444444444","44444443444444444444434444444444444444444444444444","34434443343434434444333444443443444444434444444444","34444443444444444444434444444444444444444444444444","44444443444444444444434444444444444444444444444444","45444444444444444444444444444444444454444444445444","34434443444434434444433444444444444444444444444444","34434443344434434444433444444443444444444444444444","44444444444444444444444444444444444444444444444444","44444444444444444444444444444444444444444444444444","44444444444444444444444444444444444444444444444444","34334443343434333433333344333443343343334443434333","45444544444444444444444444444544454454444444545444","44444444444444444444444444444444444444444444444444","44434443444434444444433444444444444444444444444444","44444443444434444444433444444444444444444444444444","44444443444444444444434444444444444444444444444444","45445544444445444444444455444454454454444544545444","44444444444444444444444444444444444444444444445444","34434443344434434444333444444443444444434444444444","44444444444444444444444444444444444444444444444444","44444443444434444444434444444444444444444444444444","44444443444444434444434444444444444444444444444444","44444443444434444444434444444444444444444444444444","44444444444444444444444444444444444454444444445444","34434443343434334333333344333443343344434443434333","34434443343434334444333444444443344444434444444434","44444444444444444444434444444444444444444444444444","45444544444444444444444444444444444454444444445444","34434443444434434444433444444443444444444444444444","34434443444434434444434444444444444444444444444444","44444444444444444444444444444444444444444444444444","44444444444444444444444444444444444444444444444444","44444444444444444444434444444444444444444444444444","34434443444434434444433444444444444444444444444444","34434443343434334434333444333443344444434444444433","34334433333434333333333344333443343343333433434333","34434443444434434444434444444444444444444444444444","44444444444444444444444444444444444444444444444444","45444444444444444444444444444444444454444444445444"}

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    Returns: {"47764075922906524730022932222828033263329526504894", "74603800284153925312513733013033673235009892788308", "51202729927017007247598394342529954398372135676545", "87083899296495413596111743347290367936900706289874", "65155666925625379412831001981558479081239561855507", "01814905172008216395546065755788008871615897808688", "06282185073526918376792938374317057801300800540146", "07375882369863438330527357038082652578811664618198", "89603796921676161869702996901576867747419724723003", "39552651360551024730047336891713566481353963836781", "99253230208404914143022746270190890776487805677801", "01277282036345748086237919654005148720027835783816", "32242624516908383208287282658534183440042763008504", "73730242484220557774811872533004221480752697598047", "26112808069408267682141185906430772499540953263636", "46605815836454835345814919029728778467886394708350", "18821800111636387849440263512922097428734138766030", "68352350832867315414459456020086203708495025788011", "27656702425255827336416767249791017444844578059617", "66316692665225828418112879661112591363576288935323", "66509990040547016625575215629661352468074496145699", "68009233817321320195019214158451710735624302836050", "09428088160964959992924364273096966559229546657456", "81739549710855610513677921006395276680262787528551", "00092706325283933371277156994602535249626363943162", "00119366195440262646499184419640665373074990143803", "07363755285056269720823598599512563049912400423505", "24805162885813062595894926092995834954992598899811", "69730374088592915954416123352749198583550953452493", "33948564900668651000126012415567292073782333911446", "96883866632326730052375059982692392134961375202567", "83248944565591957344942084616561243412606023257921", "21363671776525087946234076092931812080893232672513", "17841367236877212983354367957177866521522021025006", "48589250182806821232633493174392870335865775757994", "09069165000413042948712416612610051232309288734575", "45297842531722574730013207433423716592342581327362", "36808291263724224117990091241698035814169687057628", "91893145494666432552241239582628767383518996985942", "28832930411494275459033800533835947078409613183100", "58565541534947353584231733612770501674035324728442", "28750643722958012264669472239832085573261079993189", "52738025739163170564182673497848321857147372568388", "59537330058039048161812595903664270052498646503657", "04033827602531885319210766909833323915128005156668", "29412027573353590424212266864567842324750703003322", "12129625560143360456110504274323029293544049436040", "20945345068128527228452414417185658666701707080164", "81668830197443072729206984380165722688377120595892", "94159681896412628904816313640962149588498801616857" }

    A 50x50 case with entries in the answer uniformly chosen.

  10. {"87788787887788778788777778777887777877777788877878","77777777777777777777777777777777777777777777777777","77777777777777777777777777777777777777777777777777","77777777777777777777777777777777777777777777777777","87787777877787777777777777777777777777777777877778","87788787887788777788777778777887777877777788877878","77777777777777777777777777777777777777777777777777","87787787877788777787777777777777777777777777877778","77777777777777777777777777777777777777777777777777","87788787887788778788777778777887777887877788877878","87788787877788777787777778777777777877777787877878","87788787877788777787777778777777777877777787877878","77777777777777777777777777777777777777777777777777","87788787887788778788777878777887787887777788877878","87787777877787777777777777777777777777777777777778","87788787887788778788777778777887777877777788877878","87787787877788777777777777777777777777777777877778","87787787877788777777777777777777777777777777877778","77777777777777777777777777777777777777777777777777","77787777777787777777777777777777777777777777777777","77777777777777777777777777777777777777777777777777","87787777877788777777777777777777777777777777877778","77777777777777777777777777777777777777777777777777","87788787877788777787777778777777777877777787877878","88788788887788778788777878777887787887877788877878","87788787887788778788777878777887777887777788877878","88888788887788778788777878777887787887877788877878","87788787887788777787777778777777777877777788877878","77777777777777777777777777777777777777777777777777","77777777777777777777777777777777777777777777777777","77787777777777777777777777777777777777777777777777","87787787877788777777777778777777777877777787877778","87788787877788777788777778777877777877777787877878","87788787887788777788777778777887777877777788877878","87788787777788777777777777777777777777777777877778","77777777777777777777777777777777777777777777777777","77787777777777777777777777777777777777777777777777","77787777777787777777777777777777777777777777777778","77777777777777777777777777777777777777777777777777","87788787887788778788777878777887787887777788877878","87787787877788777787777778777777777877777787877778","77777777777777777777777777777777777777777777777777","88888788888888878788878878878887787887877888888878","77777777777777777777777777777777777777777777777777","77787777777787777777777777777777777777777777777777","88888888888888878788878878878887887887877888888878","87788787887788778788777778777887777877777787877878","77787777777777777777777777777777777777777777777777","77787777777787777777777777777777777777777777777777","77777777777777777777777777777777777777777777777777"}

    {"09910909009900980800999980989009998099999900099090","88898788988798868788878868778887787887877888978879","98899898998899878798888879878888887987877898988979","88898788887799878788877868878887787887877888877878","09909899099809989899989979879998898998988999089980","09900909009900989800999980989009998098988900099090","98899898988899878798878879878987887988887899988979","09909809099900989809989979989998898998988999089980","98899898998899879799888879878998887988888899988989","09910909009910980900999980989009998009099900099090","09900909099900989809999980989998998098988909099080","09900909099900989809999970989998998098988909099080","98899898988899879799878879878888887988878898988979","09910909009900980900999080989009908009999900099090","09909899099809989899889979888998898998988999989980","09910909009900980800999980989009998099999900099090","09909809098800979899989979889998898998988999089980","09909909099900989899989979989998898998988999089980","98899898998899879899888979878998887988888899988989","99909899999809989899888979879998897998988999989989","98899898988899878798888879878887787987877898988879","09909899099800989899989979989998898998988999089980","98899898998899878799888879878897887988877899988979","09900909099900989809989980989998998098988909099080","00910900009910980900999080989009908009099900099090","09900909009900980800999080989009998009999900099090","00010900009911990900999080989009908009099900099091","09900909009900989809999970989998998098998900099080","98899898998899879799888879878897887987887899988979","98898898888899878788878868778887787987877888978879","98809898998899879899888879878998887988888899988989","09909909099900989899989970989998898098988909099980","09900909099900989800999980989098998098989909099080","09910909009900989800999980989008998099999900099080","09900909999800989899989979889998898998988999089980","88798788887788768788777768767887786887877788877878","98809899998899879899888979878998897988888899988989","99909899998809979899988979878998898998988999988980","98899898998899878798888869878897887987877898988979","09910909009900980900999080989009908009999900099090","09909909099900989809989970989998898098988909099980","98898788888798868788878868778887787887877788877878","10010910100011090910090080090009909009099010100091","98899898998899879899888879878998897988888899988989","99909899998809989899889979878998897998988999988989","10011010110011090911090091090009009109099010100191","09910909009900980800999980989009998099988909099090","98809898998899879799888979878998897998888899988989","99909899998809879899889979878998897998988999989989","98899898998899879799888879878998887988888899988989"}

    {"68803548436477670841725935567332396490701530635405","91147993070819095495161368910576842826365176090840","47493337205253638829414701455990286279598338534284","93159981979731216497059469010554742925266094999759","11058883050929005376050467891766622735254085191841","56584348306484669922505802364101386499699431526105","56493337495154658829394711455099166370509510334075","04348802082031105408060488101886943947257196181860","58782337406284660930514824566201285270801440644205","68706579528607981142838944666231499402022743648316","34470014282144447528204502143899174269678407402083","24570225384253428608203780322899075157687308324064","37472325394373640811593713454990176370590439314195","79815478526687772162628034768222409612932742766306","03149783061729015376970477919564742734165174991750","69603468415496661843736824656221486582702630637215","13139802069710295385050477910555621925266176070840","14358012171021227488180568022666932956266187080750","68794547536595671032725035477131288580802650547317","80027881760819004184858256990653739715145064880629","44570226184143439729204702344998953079697218412964","23248992081842217488271468010887743836477286081841","37493127213165649831514702454919264170599420423194","24461125182164448509394501223999154059498327324163","71935561638517992063957047688552519624033952857427","79695369615485650842737013556111388400810651645216","92038690848600904174859168989654619625034865888530","46571236414253558819314692245999076278709430434093","56673245303254440821315713354908085279508330434293","14168003981021315597271488902867833057356286292961","68804358616586752052537813466212488581920750755207","13359124091131427498382670211787862068587306113872","46592236395263439811313711254198265168690439424085","46504356324466559940515722355029276280711441445384","23360003980820325587270389921666751947477185092750","70804560728698972164828944687443319603012742657508","78905650528487781144838044786331509593823752858318","91137672868628084164059268899655620635054064878730","35570215304252548529402591142909075069599217313162","99816669739598974153737257698543428622933772879537","14259004181043418517173570111978953068586316213862","02028891740718095184060357800663711723245975979728","14359903073133236608372599211877952966377207101963","68894548425585872033615935677121308480902552636215","82028871759709104376860158888454739633145075968648","24360025102253548500394500143998063057477307413073","46602358525375561721514704554211377270899439525104","57803348627375871943727034577230308300902541637305","90038691969618993264860267799564639725254073880728","57792246316376741741425904464210287391710521525204"}

    Returns: {"88789798978897979989789877887777889889998999899789", "99889787778899998779787888878977777897778797878788", "87977787987899799789878889777997777888989979778788", "97877799879977777777899787778999877798877879979879", "79978897798789988898898789997787997988889888777787", "89997887997779879797898899979897788779999987897978", "78977787797998779789998879777898897787978797978997", "97799989877788999877999879798778787887997888898879", "87799898897979878789889877777797889998787978779878", "99997878997778779799787979899989897988788897997989", "89889999899897879979977977978987778787798799799878", "99789788797788898899978799799987877899789898877897", "97998799898779787797799877778997887787987878998877", "88888979999798988779997889797998887778878898879999", "87887997787989978898978779879989877989978799977878", "87989878999878988987778988798888799797997899897979", "77897878789998798889898779878998998798877797898788", "87789779788798877897879799877998798878988897999989", "88898799878779978798789777977978997799897879987877", "99898788977788878979989889787789779897887798977898", "79789787997898887778977777777888999977779988789997", "78899899878977887897788899889777987998777798998898", "97977997979987788777778888778978799987988887889878", "99898888999877878998887978898887798997978879877798", "97879997998979879989779987988779888877888799899989", "77997977799889999988777799898998897879889878889978", "87887979899997978989988977798788899987998997979987", "88899888778899879799978998987998987889778877878979", "78797879889898987787977877878989978888979977878779", "87979788978798789788788879997797897777898798787778", "88788988798788897778977999988897797798779779779987", "99899778979799788998788798799988979877778789977978", "88878888897889998797979879978799798999887878888987", "99977879979797989779888979988979898988877977978799", "78777788979999779798789978978998979887777899987989", "87899887797787788777797979878777977787798898988797", "89798797997998979797787879779889787897987888787987", "88788997879979898999788877888787888977978798989787", "88789798777789778978779988979877877987877989888799", "79998899897998897899999777978788979879988979877879", "98999898889887797879997898899797888877779779877988", "77897778997889887979777788877779797889787887888799", "98899999997797979788798879799898889979988888989887", "88798798989789777797899877777988877899797977898979", "97897798988898778787977987899988779979887787899879", "99999988979788778997887979978888889999999899788888", "99879877778888977998889997789787797998799989898979", "99789998787999778887787778877879877979797988897889", "89887978778989989899977878988878879887778789977799", "88789989987887797978978797879788887877878897898879" }

    50x50 case with answer entries randomly chosen from [7,9].

  11. {"0000000","0000000","0000000","0000000","0000000","0000000","0000000"}

    {"6666786","5544554","5655565","6665665","5555665","5544564","7767786"}

    {"7865614","1027571","3076722","1015080","6873063","1466215","0185302"}

    Returns: {"8978354", "0372053", "7212791", "2506766", "5526561", "2155531", "7870888" }

    A smaller test case, this is the base for modifications to have NO SOLUTION test cases later on.

  12. {"0000000","0000000","0000000","0000000","0000000","0000000","0000000"}

    {"6666786","5544554","5655565","6665665","5555665","5544564","7767786"}

    {"7865614","1027571","3076722","1015080","6873063","1466215","0185301"}

    Returns: {"NO SOLUTIONS" }

    The lower right entry was decreased by one, should be caught by "sum of all entries in answer" modulus check.

  13. {"0000000","0000000","0000000","0000000","0000000","0000000","0000000"}

    {"6666786","5544554","5655565","6665665","5555665","5544564","7767786"}

    {"7865614","1027571","3076722","1015080","6873063","1466215","0185311"}

    Returns: {"NO SOLUTIONS" }

    This case passes "sum of all entries" check, but fails the row and column checks.

  14. {"1111111","1111111","1111111","1111111","1111111","1111111","1111111"}

    {"3324333","4334443","3223332","3223333","3334333","3223333","3223333"}

    {"7181957","2142319","1442537","2759566","7101757","7785544","2356642"}

    Returns: {"NO SOLUTIONS" }

    An otherwise valid test case, but the answer does not correspond to a valid number grid (some entries are >9).

  15. {"0000000","0000000","0000000","0000000","0000000","0000000","0000000"}

    {"5454554","5555665","4443454","5655665","5443554","5554664","6544664"}

    {"9803489","9591072","3847953","9123488","0426340","4849307","1984058"}

    Returns: {"NO SOLUTIONS" }

    The upper left entry in the answer is -1, making the solution invalid.

  16. {"23333333333322333333333333333333333333333333333332", "33333333343333333333333333333333334333333333443333", "12222222222211221222222222222222222222222222222221", "12222222222211221122222221111221222222112222222221", "12222222222211221122222221111221222222112222222221", "12222222222211221122222221111221222222112222222221", "12222222222211221122222221111221222222112222222221", "22222222232222222222222222222222223222222222232222", "12222222222222222222222222222222222222222222232221", "01111111111100110011111110000110111111001111111110", "01111111111100110011111110000110111111001111111110", "22222222232222222222222222222222223222222222332222", "22222222232222222222222222222222222222222222232222", "12222222222222222222222222222222222222222222222221", "11111112221111111112221111111111112222111112222211", "12221112222211221122222221111221222222112222222221", "11111112222211111122221221111221222222111222222221", "22222223333322322233332332222332333333222223333322", "33333333343333333333333333333333333333333333343333", "01111111111100110011111110000110111111001111111110", "01111111111100110011111110000110111111001111111110", "01111111111100110011111110000110111111001111111110"}

    {"81221116682299220134442330000331447555001226795438", "14554449915522553457764553333554770777335559027651", "81221116682299229123331330011221336334111226783318", "60110004461188118901120119999119225223990115672106", "60110004461188118901120119999119225223990115672106", "60110004461188118901120119999119225223990115672106", "60110004461188118901120119999119225223990115572116", "14554448805522552356663663333553660667334558916651", "93333337793311331235542331111442558666112337806539", "70110005571188118912220229999229226334990115683217", "70110005571188118912220229999229226334990115683217", "15554449916633663356665663344663660888445659028761", "03443338803311431246653452233542558667333338806640", "92332227782200220134442331111331337556111236795439", "48998883348866896790008996677997993111778992351094", "60119994461188018912220119999119115333990114573216", "69999994460077997901119008899119114223999003462106", "68999994460077096801108008888008004112888993461096", "03443338804422552345554553333553559667333448916540", "70110005571188118912220229999229226334990115683217", "70110005571188118912220229999229226334990115683217", "70110005571188118912220229999229226334990115683217"}

    {"86336665563355332604443002299076449111996335231408", "64114443341133110482254880077884227229771883012586", "38558880015577557152228224411551997996118557489283", "94114446671133113748854880077887553552774113045849", "94114446671133113748854880077887553552774113045849", "94114446671133113748854880077887553552774113045849", "94114446671133113748854880077887553552774113345819", "16336668893355335930009002222339772774226338567731", "72992224459911991593365991188665338007885224190397", "16336665563355335937776002299009772441996335234731", "16336665563355335937776002299009772441996335234731", "83336665560022002937773779966779772118663035231408", "49669998829988691560032635522365338774229991897064", "05225554485544554826665221188228994330888527453620", "83003332263322302604443709966776772118663005231408", "94117776671133413715554810077887883229774116342519", "20777776674466776048887443300110116552007449675842", "08555554452244257126698291188221994663888557456950", "97447776674433113048884880077110883552777446345849", "16336665563355335937776002299009772441996335234731", "16336665563355335937776002299009772441996335234731", "16336665563355335937776002299009772441996335234731"}

    Returns: {"18888888888888881111111888888811111118888888881111", "18888888888888881111188888888881111888881118888811", "11111118881111111118881111111881118888111111188881", "11111118881111111188811111111111118888111111188881", "11111118881111111188811111111111118888111111188881", "11111118881111111188811111111111118888111111188881", "11111118881111111188811111111111118888111111888811", "11111118881111111118888111188881111888881118888111", "11111118881111111111188888888111111111888888811111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11888888881111111888881111111118888111111188881111", "11111111188811188811188811111188888111111888881111", "11111111188811881111111881111881888111118818881111", "11111111188811811111111181111111888111111118881111", "11118888881111811111111181111111888111111118881111", "18881111111111881111111881111111888111111118881111", "18881111111111188811188811111888888888118888888881", "18888888888811111888881111111888888888118888888881", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111111" }

  17. {"11111111111111111111111111111111111111111111111111"}

    {"88888888888888888888888888888888888888888888888888"}

    {"33333333333333333333333333333333333333333333333333"}

    Returns: {"605529602 SOLUTIONS" }

  18. {"2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2","2"}

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    {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

    Returns: {"609020967 SOLUTIONS" }

  19. {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

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    Returns: {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" }

  20. {"4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4"}

    {"5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5"}

    {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

    Returns: {"9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9" }

  21. {"4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4","4"}

    {"5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5","5"}

    {"1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1"}

    Returns: {"NO SOLUTIONS" }

  22. {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

    {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}

    {"1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1","1"}

    Returns: {"50 SOLUTIONS" }

  23. {"3322333333333333333333323332333333233","3322333333333333333333323333333333233","3323333333333333333333323332333333233","2222233222222222233232223222232222222","3323333333333333333333333333333333333","3222233233333322333233323232232332223","3333333333333333333333333333333333333","3222333233333323333333323332232332233","3323333333333333333333323333333333233","3222333233333333333333323332232333233","3222233233323322333232323222232232222","3322333333333333333333323332333333233","3323333333333333333333333333333333333","3222333333333333333333323332333333233","3323333333333333333333323333333333233","3222333233333323333333323332233333233","3222233233323322333232223222232232222","3222233233323322333333323232232232223","3222233233222322333232223222232232222","2222223222222222222232223222222222222","3322333333333333333333323332233333233","3333333333333333333333333333333333333","3322333233333333333333323332233333233","2222233233323322333232323222232232222","3222333233333333333333323332232333233","3333333333333333333333333333333333333","2222233223222222233232223222232222222","3222333233333323333333323332232332233","3222233233323323333232323232232232223","3333333333333333333333333333333333333","3323333333333333333333333333333333333","3322333333333333333333323332233333233","3323333333333333333333323333333333233","3323333333333333333333323332333333233","2222233233323323333232323222232332223"}

    {"2079144023212202233141284129030231812","3189145033222312344252295220031232812","3080155133323312344152295129031231913","9746811699979978900808851886607997579","4281266144433423455263406231141342033","0857923801100199021920062907818019690","4301477356545534566474417442362453135","1968034922201190222031183018929029701","3180246133323422344153295120031332923","1968044923201201232031184118929120711","0757922800090089011919062896707908699","2079145033223312333142294129030231812","4291366245434423455363407331252342034","2979144033212201333141285029020221811","4190256234423413454253396231142332923","1968034921101191223031174008810010701","0847812800090089011929962897717908599","1867923911090199122020062908819919691","0757812800989079011819962896707908599","8525690588768866898607740674585785367","2079045033212201343141284119930131812","5402478356555535667475527442363564245","2079144923212201233132185119930230811","9757912800080089011929062996708908599","1968034912101201222031183008829020701","4302477356535534565364517341363454045","9736811790979978900707951886607897489","0968033811101290222030173007919019701","0857923811090090112929062907818909690","6524589577766757788696739674485686257","3290356244324423455353406341142342034","2169145033212311343141285029930221812","3180256034323322445152395120031231923","2180256144322313444252395229041331913","9857922810090180121929072997708009690"}

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    Returns: {"1127159387409530849833529549146142087", "4218996704739286761454951240092810857", "0823932096444874873600875537941684054", "3330054746170284985264604013825013081", "3474965688269233758765223840258655119", "9114583560003427827191379715083423406", "9229359635855965478619719082119738580", "4288813407181648458491105602172738192", "7440092558358019754950925642878270646", "8488823660454030367666335075285350507", "1602213165515403321374356586758734218", "9929477933801520595444727734254056342", "3330248760641888898448893280218989107", "4927518125856456437773512711190280578", "1902481088398167438552664802361596877", "8453651329163943081762453471780782005", "4262678346510241450200831365029198619", "1807237031775348541193597450342812551", "0400665159568286130551600524738434216", "0250354434361428005914122512103108497", "4742953135992977339156446082535722070", "6117748994917867874533339985324665085", "4120258974032988754490770473822024459", "8613289098060504352107043266474253505", "5142743563614520359192118792872735146", "8635219231786983799987457767022732723", "0143059171684104511589319190700713900", "7530014756156213378058557249090388206", "1600593642254621572038745026065772592", "8754799188929662897386088428950624784", "8508486286992457764188229201366784316", "1098594506314309609575664816508265471", "5464153942516905060928223872599679472", "8412523416549991348657719249554186090", "9160279217717230112147409476990164313" }

  24. {"3322333333333333333333323332333333233","3322333333333333333333323333333333233","3323333333333333333333323332333333233","2222233222222222233232223222232222222","3323333333333333333333333333333333333","3222233233333322333233323232232332223","3333333333333333333333333333333333333","3222333233333323333333323332232332233","3323333333333333333333323333333333233","3222333233333333333333323332232333233","3222233233323322333232323222232232222","3322333333333333333333323332333333233","3323333333333333333333333333333333333","3222333333333333333333323332333333233","3323333333333333333333323333333333233","3222333233333323333333323332233333233","3222233233323323333233223222232332222","3222233233323322333333323232232232223","3222233233222322333232223222232232222","2222223222222222222232223222222222222","3322333333333333333333323332233333233","3333333333333333333333333333333333333","3322333233333333333333323332233333233","2222233233323322333232323222232232222","3222333233333333333333323332232333233","3333333333333333333333333333333333333","2222233223222222233232223222232222222","3222333233333323333333323332232332233","3222233233323323333232323232232232223","3333333333333333333333333333333333333","3323333333333333333333333333333333333","3322333333333333333333323332233333233","3323333333333333333333323333333333233","3323333333333333333333323332333333233","2222233233323323333232323222232332223"}

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    {"7851646550690994792069594100234303701","0326465799926804436004728065944291597","4711429407211216324858804778095427390","1204307757585806212294075292111098363","2271507926507968550804567576899567346","0975323488107118825812855045408133493","7537224080022347941061182445049595086","5801093541029997294512029158319828707","0427692278630304776831087996491164031","4934316611089838618670122018539539625","3932148338140687876184323729288377136","2382651237521237379781629248459722779","5648557177458646743454220469162566681","3940176601132967093018490827179154109","0309647182034690436673782170342282244","0525144518936581550130660278690763783","2594905379367061969470860162139135957","0404891139657419323032859522361966560","2912574122975682845785857569086455916","0940663625950228758100113359499569513","5347953813218668313857788778956834829","5194380276415990090692017097389113036","2636325741845324665280121054336209117","6921172405695586845351636049562858849","4947163485596015393811016068619821753","7010253373080218519682333659025480732","4491302322071986686979360115236398444","9226569969721099041622344288168945360","8489313306956914170975489734426884307","9113995648069751633405924110319710993","8258197439985855655592672226892549250","8091312442896236043438560944983391428","2403531884472418460863789766770765205","9455161310449422182134293399715258687","8707415519271183318644503162379270364"}

    Returns: {"NO SOLUTIONS" }

  25. {"3322333333333333333333323332333333233","3322333333333333333333323333333333233","3323333333333333333333323332333333233","2222233222222222233232223222232222222","3323333333333333333333333333333333333","3222233233333322333233223232232332223","3333333333333333333333333333333333333","3222333233333323333333323332232332233","3323333333333333333333323333333333233","3222333233333333333333323332232333233","3222233233323322333232223222232232222","3322333333333333333333323332333333233","3323333333333333333333333333333333333","3222333333333333333333323332333333233","3323333333333333333333323333333333233","3222333233333323333333323332233333233","2222233222222222233232223222232222222","3222233233323322333333223232232232223","3222233233222322333232223222232232222","2222223222222222222232223222222222222","3322333333333333333333323332233333233","3333333333333333333333333333333333333","3322333233333333333333323332233333233","2222233233323322333232223222232232222","3222333233333333333333323332232333233","3333333333333333333333333333333333333","2222233223222222233232223222232222222","3222333233333323333333323332232332233","3222233233323323333232223232232232223","3333333333333333333333333333333333333","3323333333333333333333333333333333333","3322333333333333333333323332233333233","3323333333333333333333323333333333233","3323333333333333333333323332333333233","2222233233323323333232223222232332223"}

    {"2079144023212202233141184129030231812","3189145033222312344252195220031232812","3080155133323312344152195129031231913","9746811699979978900808751886607997579","4281266144433423455263306231141342033","0857923801100199021920962907818019690","4301477356545534566474417442362453135","1968034922201190222031083018929029701","3180246133323422344153195120031332923","1968044923201201232031184118929120711","0757922800090089011919962896707908699","2079145033223312333142194129030231812","4291366245434423455363307331252342034","2979144033212201333141185029020221811","4190256234423413454253296231142332923","1968034921101191223031074008810010701","9736701799989979900818851886706997488","1867923911090199122020962908819919691","0757812800989079011819862896707908599","8525690588768866898607740674585785367","2079045033212201343141184119930131812","5402478356555535667475427442363564245","2079144923212201233132185119930230811","9757912800080089011929962996708908599","1968034912101201222031083008829020701","4302477356535534565364417341363454045","9736811790979978900707851886607897489","0968033811101290222030073007919019701","0857923811090090112929962907818909690","6524589577766757788696639674485686257","3290356244324423455353306341142342034","2169145033212311343141185029930221812","3180256034323322445152295120031231923","2180256144322313444252295229041331913","9857922810090180121929972997708009690"}

    {"7851646550690994792069494100234303701","0326465799926804436004628065944291597","4711429407211216324858704778095427390","1204307757585806212294975292111098363","2271507926507968550804467576899567346","0975323488107118825812755045408133493","7537224080022347941061082445049595086","5801093541029997294512929158319828707","0427692278630304776831987996491164031","4934316611089838618670022018539539625","3932148338140687876184223729288377136","2382651237521237379781529248459722779","5648557177458646743454120469162566681","3940176601132967093018390827179154109","0309647182034690436673682170342282244","0525144518936581550130560278690763783","1483894268256950858369759051028024846","0404891139657419323032759522361966560","2912574122975682845785757569086455916","0940663625950228758100013359499569513","5347953813218668313857688778956834829","5194380276415990090692917097389113036","2636325741845324665280021054336209117","6921172405695586845351536049562858849","4947163485596015393811916068619821753","7010253373080218519682233659025480732","4491302322071986686979260115236398444","9226569969721099041622244288168945360","8489313306956914170975389734426884307","9113995648069751633405824110319710993","8258197439985855655592572226892549250","8091312442896236043438460944983391428","2403531884472418460863689766770765205","9455161310449422182134193399715258687","8707415519271183318644403162379270364"}

    Returns: {"NO SOLUTIONS" }

  26. {"3322333333333333333333323332333333233","3322333333333333333333323333333333233","3323333333333333333333323332333333233","2222233222222222233232223222232222222","3323333333333333333333333333333333333","3222233233333322333233223232232332223","3333333333333333333333333333333333333","3222333233333323333333323332232332233","3323333333333333333333323333333333233","3222333233333333333333323332232333233","3222233233323322333232223222232232222","3322333333333333333333323332333333233","3323333333333333333333333333333333333","3222333333333333333333323332333333233","3323333333333333333333323333333333233","3222333233333323333333323332233333233","2222233222222222233232223222232222222","3222233233323322333333223232232232223","3222233233222322333232223222232232222","2222223222222222222232223222222222222","3322333333333333333333323332233333233","3333333333333333333333333333333333333","3322333233333333333333323332233333233","2222233233323322333232223222232232222","3222333233333333333333323332232333233","3333333333333333333333333333333333333","2222233223222222233232223222232222222","3222333233333323333333323332232332233","3222233233323323333232223232232232223","3333333333333333333333333333333333333","3323333333333333333333333333333333333","3322333333333333333333323332233333233","3323333333333333333333323333333333233","3323333333333333333333323332333333233","2222233233323323333232223222232332223"}

    {"2079144023212202233141184129030231812","3189145033222312344252195220031232812","3080155133323312344152195129031231913","9746811699979978900808751886607997579","4281266144433423455263306231141342033","0857923801100199021920962907818019690","4301477356545534566474417442362453135","1968034922201190222031083018929029701","3180246133323422344153195120031332923","1968044923201201232031184118929120711","0757922800090089011919962896707908699","2079145033223312333142194129030231812","4291366245434423455363307331252342034","2979144033212201333141185029020221811","4190256234423413454253296231142332923","1968034921101191223031074008810010701","9736701799989979900818851886706997488","1867923911090199122020962908819919691","0757812800989079011819862896707908599","8525690588768866898607740674585785367","2079045033212201343141184119930131812","5402478356555535667475427442363564245","2079144923212201233132185119930230811","9757912800080089011929962996708908599","1968034912101201222031083008829020701","4302477356535534565364417341363454045","9736811790979978900707851886607897489","0968033811101290222030073007919019701","0857923811090090112929962907818909690","6524589577766757788696639674485686257","3290356244324423455353306341142342034","2169145033212311343141185029930221812","3180256034323322445152295120031231923","2180256144322313444252295229041331913","9857922810090180121929972997708009690"}

    {"7851647550690994791069494100234303701","0326465799926804436004628065944291597","4711429407211216324858704778095427390","1204307757585806212294975292111098363","2271507926507968550804467576899567346","0975323488107118825812755045408133493","7537224080022347941061082445049595086","5801093541029997294512929158319828707","0427692278630304776831987996491164031","4934316611089838618670022018539539625","3932148338140687876184223729288377136","2382651237521237379781529248459722779","5648557177458646743454120469162566681","3940176601132967093018390827179154109","0309647182034690436673682170342282244","0525144518936581550130560278690763783","1483894268256950858369759051028024846","0404891139657419323032759522361966560","2912574122975682845785757569086455916","0940663625950228758100013359499569513","5347953813218668313857688778956834829","5194380276415990090692917097389113036","2636325741845324665280021054336209117","6921172405695586845351536049562858849","4947163485596015393811916068619821753","7010253373080218519682233659025480732","4491302322071986686979260115236398444","9226569969721099041622244288168945360","8489313306956914170975389734426884307","9113995648069751633405824110319710993","8258197439985855655592572226892549250","8091312442896236043438460944983391428","2403531884472418460863689766770765205","9455161310449422182134193399715258687","8707415519271183318644403162379270364"}

    Returns: {"NO SOLUTIONS" }

  27. {"111111211111","111111111111","111111111111","212212212121","112112212121","112112211111","111111111111","212212211121","222212212121","112112211121","111111111111","222212212121","111111211111","212212212121","111111111111","112212211121","112111211111","112212211121","111111111111","111111111111","111111111111","112112211121","112212211121","112111211121","212212212121","222212212121","212212212121","222212212121","111111111111"}

    {"889979058686","779869948586","879778957586","080090160708","990990070708","980980069797","879878958696","090080069708","001091180819","980980069708","889878958696","101091280819","879879068686","091091170819","889979958686","991081179818","980879069697","991080179708","767768847586","979879968696","868868848585","980980079708","991080179708","980989069707","091091170818","001191170808","092191180818","101191280819","768867847586"}

    {"901191267785","903290071891","451924128652","373001050423","837713620921","552743151678","064209885029","015379695734","844856614553","371830861701","818408487467","507983348545","297931019194","355664572851","404020647692","800870287011","264987154780","654353236427","079764456140","049481817059","085044690875","457955435613","830788848648","991558977817","880424281323","442370696097","462325503459","245243218423","775077632541"}

    Returns: {"239206063198", "560430582315", "012706435554", "089518492672", "636917933285", "466432957083", "843865112521", "458351968472", "629874949653", "758456358061", "211888732305", "188969437883", "832355100678", "996844869133", "514155461069", "996183609428", "421965621648", "920488438890", "838300541400", "191916413824", "155353630008", "894553906371", "966275048891", "249849353066", "249862938449", "809138745997", "990294949646", "339598456894", "243108476110" }

  28. {"111111211111","111111111111","111111111111","212212212121","112112212121","112112211111","111111111111","212212211121","222212212121","112112211121","111111111111","222212212121","111111211111","212212212121","111111111111","112212211121","112111211111","112212211121","111111111111","111111111111","111111111111","112112211121","212212212121","112111211121","212212212121","222212212121","212212212121","222212212121","111111111111"}

    {"889979058686","779869948686","879778957586","080090160708","990990070808","980980069797","879878958696","090080069708","001091180819","980980069708","889878958696","101091280819","879879068686","091091170919","889979958686","991081179818","980879069697","991080179708","767768847586","979879968696","868868848685","980980079708","091091270709","980989069807","091091170818","001191170808","092191180818","101191280819","768867847586"}

    {"901191267985","903290071091","451924128852","373001050623","837713620121","552743151878","064209885229","015379695934","844856614753","371830861901","818408487667","507983348745","297931019394","355664572051","404020647892","800870287211","264987154980","654353236627","079764456340","049481817259","085044690075","457955435813","052900060860","991558977017","880424281523","442370696297","462325503659","245243218623","775077632741"}

    Returns: {"NO SOLUTIONS" }

  29. {"111111211111","111111111111","111111111111","212212212121","112112212121","112112211111","111111111111","212212211121","222212212121","112112211121","111111111111","222212212121","111111211111","212212212121","111111111111","112212211121","112111211111","112212211121","111111111111","111111111111","111111111111","112112211121","112111211111","112111211121","212212212121","222212212121","212212212121","222212212121","111111111111"}

    {"889979058586","779869948486","879778957486","080090160608","990990070708","980980069697","879878958596","090080069608","001091180719","980980069608","889878958596","101091280719","879879068586","091091170719","889979958586","991081179718","980879069597","991080179608","767768847486","979879968596","868868848485","980980079608","880979068697","980989069607","091091170718","001191170708","092191180718","101191280719","768867847486"}

    {"901191267885","903290071991","451924128752","373001050523","837713620021","552743151778","064209885129","015379695834","844856614653","371830861801","818408487567","507983348645","297931019294","355664572951","404020647792","800870287111","264987154880","654353236527","079764456240","049481817159","085044690975","457955435713","941899959759","991558977917","880424281423","442370696197","462325503559","245243218523","775077632641"}

    Returns: {"NO SOLUTIONS" }

  30. {"111111211111","111111111111","111111111111","212212212121","112112212121","112112211111","111111111111","212212211121","222212212121","112112211121","111111111111","222212212121","111111211111","212212212121","111111111111","112212211121","112111211111","112212211121","111111111111","111111111111","111111111111","112112211121","112111211111","112111211121","212212212121","222212212121","212212212121","222212212121","111111111111"}

    {"889979058586","779869948486","879778957486","080090160608","990990070708","980980069697","879878958596","090080069608","001091180719","980980069608","889878958596","101091280719","879879068586","091091170719","889979958586","991081179718","980879069597","991080179608","767768847486","979879968596","868868848485","980980079608","880979068697","980989069607","091091170718","001191170708","092191180718","101191280719","768867847486"}

    {"901191267885","903290071991","451924128752","373001050523","837713620021","552743151778","064209885129","015379695834","844856614653","371830861801","818408487567","507983348645","397931019294","355664572951","404020647792","800870287111","264987154880","654353236527","079764456240","049481817159","085044690975","457955435713","941899959759","891558977917","880424281423","442370696197","462325503559","245243218523","775077632641"}

    Returns: {"NO SOLUTIONS" }

  31. {"0","0","0"}

    {"0","2","0"}

    {"7","9","6"}

    Returns: {"NO SOLUTIONS" }

  32. {"0","0","0","0","0"}

    {"5","2","1","2","5"}

    {"1","7","9","1","7"}

    Returns: {"NO SOLUTIONS" }

  33. {"00"}

    {"12"}

    {"15"}

    Returns: {"NO SOLUTIONS" }

  34. {"0","0","0","0"}

    {"1","0","2","2"}

    {"4","6","6","2"}

    Returns: {"NO SOLUTIONS" }

  35. {"0","0","0","0"}

    {"1","2","2","0"}

    {"0","6","8","8"}

    Returns: {"NO SOLUTIONS" }

  36. {"7","7"}

    {"6","6"}

    {"3","3"}

    Returns: {"NO SOLUTIONS" }

  37. {"66"}

    {"00"}

    {"55"}

    Returns: {"NO SOLUTIONS" }

  38. {"00","00"}

    {"00","00"}

    {"31","44"}

    Returns: {"00", "31" }

  39. {"00","00"}

    {"00","10"}

    {"52","37"}

    Returns: {"NO SOLUTIONS" }

  40. {"0000","0000"}

    {"0000","0000"}

    {"1068","4533"}

    Returns: {"NO SOLUTIONS" }

  41. {"00","00"}

    {"98","94"}

    {"81","60"}

    Returns: {"NO SOLUTIONS" }

  42. {"00","00","00","00"}

    {"00","00","00","00"}

    {"76","75","44","66"}

    Returns: {"NO SOLUTIONS" }

  43. {"0000","0000"}

    {"0000","0000"}

    {"0000","1010"}

    Returns: {"NO SOLUTIONS" }

  44. {"000","000"}

    {"000","000"}

    {"433","030"}

    Returns: {"NO SOLUTIONS" }

  45. {"00","00","00"}

    {"00","00","00"}

    {"85","96","94"}

    Returns: {"NO SOLUTIONS" }

  46. {"00","00","00"}

    {"00","00","00"}

    {"00","10","00"}

    Returns: {"NO SOLUTIONS" }

  47. {"00"}

    {"00"}

    {"76"}

    Returns: {"NO SOLUTIONS" }

  48. {"00000"}

    {"13343"}

    {"66519"}

    Returns: {"NO SOLUTIONS" }

  49. {"0","0","0"}

    {"0","0","0"}

    {"8","4","8"}

    Returns: {"NO SOLUTIONS" }

  50. {"0","0","0"}

    {"1","1","0"}

    {"6","7","4"}

    Returns: {"NO SOLUTIONS" }

  51. {"0"}

    {"0"}

    {"0"}

    Returns: {"0" }

  52. {"0"}

    {"0"}

    {"9"}

    Returns: {"9" }

  53. {"000"}

    {"000"}

    {"000"}

    Returns: {"000" }

  54. {"0"}

    {"0"}

    {"7"}

    Returns: {"7" }

  55. {"00"}

    {"11"}

    {"88"}

    Returns: {"99" }

  56. {"00","00","00"}

    {"00","00","00"}

    {"00","00","00"}

    Returns: {"00", "00", "00" }

  57. {"00","00"}

    {"00","00"}

    {"11","10"}

    Returns: {"10", "00" }

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: