Thursday, July 28, 2016

Branch Cipher Part 2: Brute Force



Trying to guess the logic and key of the branch cipher, I decided to make up a very simple rule for the branches and how to generate a value for each tree. The simple rules are that the 4 types of branches (pointing up and to the left, pointing down and to the left, pointing up and to the right, pointing down and to the right), would each be assigned a value, and the values for each tree would be added up to give us an input for a A1Z26 cipher, and from there other ciphers popular with Gravity Falls creators could be applied. But what values to assign?  If each branch is assigned a random value from 1 to 26, there will be more than 450k keys to try. To try and slim down the number of attempted keys, some limits were put in place:
the values to allow for similar number of branches as seen in the drawing, allow for any number 1-26 to be encoded, and avoid keys that will obviously have the trees result in values greater than 26.

So the lowest value needed to be 1 (how else would we encode 1?), the next one could either be a 2, or a 3 since we can encode 2 with two ones, and the picture does indeed show two of the same "value" branches on each tree. 4 is too much for second lowest value because we would regularly need 3 ones to encode some values.  Similar logic was used to come up with complete list of potential key values shown in the diagram below.





We now have 30 sets of numbers to use as keys. If we try every combination of placing these keys,(4! or 4*3*2*1 = 24), there will be 720 different key orders to try. We will assume that the two smallest key values will be on the same side (left or right), otherwise there could be excessive grouping of branches for some coded values (something not seen in the drawing). This limit drops the potential key orders by 2/3 to 240.

To see how a key order (like LU=1; LD=2; RU=4; RD=8, the binary key) is applied, look at the image below.

We are not just interested in A1Z26 though, and we want to make sure if we happen on the right key that we will see the final message so as to pick it out of the crowd, so Atbash, Caesar and Combination ciphers (and the reverse of each!) will be generated. That's 8 deciphering attempts for each key order, which comes to 1920 decryption messages to sort through. Some of these have trees that result in values greater than 26, and I am assuming we want to ignore those keys orders as potential final keys.

See all 1920 attempts at deciphering using these simple rules and limited key set. See if you can find one with some meaning.

I've only given these a cursory look and did a quick text search for the words "park" and "city" with nothing popping up.

(Note: "*" means that tree value was greater than 26, and that key order can be ignored. You can see as the key values go up, so the chances that tree resulted in a value greater than 26.)

Key Key Order A1Z26 Frwd ATBASH Frwd:   CAESAR Frwd:   Combined Frwd:   A1Z26 Rvsd ATBASH Rvsd CAESAR Rvsd Combined Rvsd
1,2,4,8 LU=1; LD=2; RU=4; RD=8 PEDJGFLAD KVWQTUOZW MBAGDCIXA HSTNQRLWT DALFGJDEP WZOUTQWVK AXICDGABM TWLRQNTSH
LU=2; LD=1; RU=4; RD=8 PFDIGEJBB KUWRTVQYY MCAFDBGYY HRTOQSNVV BBJEGIDFP YYQVTRWUK YYGBDFACM VVNSQOTRH
LU=1; LD=2; RU=8; RD=4 HIHFKJHAD SRSUPQSZW EFECHGEXA POPRMNPWT DAHJKFHIH WZSQPUSRS AXEGHCEFE TWPNMRPOP
LU=2; LD=1; RU=8; RD=4 HJHEKIFBB SQSVPRUYY EGEBHFCYY PNPSMORVV BBFIKEHJH YYURPVSQS YYCFHBEGE VVROMSPNP
LU=4; LD=8; RU=1; RD=2 DEAJMIRDP WVZQNRIWK ABXGJFOAM TSWNKOFTH PDRIMJAED KWIRNQZVW MAOFJGXBA HTFOKNWST
LU=8; LD=4; RU=1; RD=2 DIAFMEJHH WRZUNVQSS AFXCJBGEE TOWRKSNPP HHJEMFAID SSQVNUZRW EEGBJCXFA PPNSKRWOT
LU=4; LD=8; RU=2; RD=1 BFBINJQDP YUYRMQJWK YCYFKGNAM VRVOJNGTH PDQJNIBFB KWJQMRYUY MANGKFYCY HTGNJOVRV
LU=8; LD=4; RU=2; RD=1 BJBENFIHH YQYVMURSS YGYBKCFEE VNVSJROPP HHIFNEBJB SSRUMVYQY EEFCKBYGY PPORJSVNV
1,2,4,9 LU=1; LD=2; RU=4; RD=9 REDKGFMAD IVWPTUNZW OBAHDCJXA FSTMQRKWT DAMFGKDER WZNUTPWVI AXJCDHABO TWKRQMTSF
LU=2; LD=1; RU=4; RD=9 RFDJGEKBB IUWQTVPYY OCAGDBHYY FRTNQSMVV BBKEGJDFR YYPVTQWUI YYHBDGACO VVMSQNTRF
LU=1; LD=2; RU=9; RD=4 HJIFLKHAD SQRUOPSZW EGFCIHEXA PNORLMPWT DAHKLFIJH WZSPOURQS AXEHICFGE TWPMLRONP
LU=2; LD=1; RU=9; RD=4 HKIELJFBB SPRVOQUYY EHFBIGCYY PMOSLNRVV BBFJLEIKH YYUQOVRPS YYCGIBFHE VVRNLSOMP
LU=4; LD=9; RU=1; RD=2 DEAKNJTDR WVZPMQGWI ABXHKGQAO TSWMJNDTF RDTJNKAED IWGQMPZVW OAQGKHXBA FTDNJMWST
LU=9; LD=4; RU=1; RD=2 DJAFNEJIH WQZUMVQRS AGXCKBGFE TNWRJSNOP HIJENFAJD SRQVMUZQW EFGBKCXGA PONSJRWNT
LU=4; LD=9; RU=2; RD=1 BFBJOKSDR YUYQLPHWI YCYGLHPAO VRVNIMETF RDSKOJBFB IWHPLQYUY OAPHLGYCY FTEMINVRV
LU=9; LD=4; RU=2; RD=1 BKBEOFIIH YPYVLURRS YHYBLCFFE VMVSIROOP HIIFOEBKB SRRULVYPY EFFCLBYHY POORISVMV
1,2,4,10 LU=1; LD=2; RU=4; RD=10 TEDLGFNAD GVWOTUMZW QBAIDCKXA DSTLQRJWT DANFGLDET WZMUTOWVG AXKCDIABQ TWJRQLTSD
LU=2; LD=1; RU=4; RD=10 TFDKGELBB GUWPTVOYY QCAHDBIYY DRTMQSLVV BBLEGKDFT YYOVTPWUG YYIBDHACQ VVLSQMTRD
LU=1; LD=2; RU=10; RD=4 HKJFMLHAD SPQUNOSZW EHGCJIEXA PMNRKLPWT DAHLMFJKH WZSONUQPS AXEIJCGHE TWPLKRNMP
LU=2; LD=1; RU=10; RD=4 HLJEMKFBB SOQVNPUYY EIGBJHCYY PLNSKMRVV BBFKMEJLH YYUPNVQOS YYCHJBGIE VVRMKSNLP
LU=4; LD=10; RU=1; RD=2 DEALOKVDT WVZOLPEWG ABXILHSAQ TSWLIMBTD TDVKOLAED GWEPLOZVW QASHLIXBA DTBMILWST
LU=10; LD=4; RU=1; RD=2 DKAFOEJJH WPZULVQQS AHXCLBGGE TMWRISNNP HJJEOFAKD SQQVLUZPW EGGBLCXHA PNNSIRWMT
LU=4; LD=10; RU=2; RD=1 BFBKPLUDT YUYPKOFWG YCYHMIRAQ VRVMHLCTD TDULPKBFB GWFOKPYUY QARIMHYCY DTCLHMVRV
LU=10; LD=4; RU=2; RD=1 BLBEPFIJH YOYVKURQS YIYBMCFGE VLVSHRONP HJIFPEBLB SQRUKVYOY EGFCMBYIY PNORHSVLV
1,2,4,11 LU=1; LD=2; RU=4; RD=11 VEDMGFOAD EVWNTULZW SBAJDCLXA BSTKQRIWT DAOFGMDEV WZLUTNWVE AXLCDJABS TWIRQKTSB
LU=2; LD=1; RU=4; RD=11 VFDLGEMBB EUWOTVNYY SCAIDBJYY BRTLQSKVV BBMEGLDFV YYNVTOWUE YYJBDIACS VVKSQLTRB
LU=1; LD=2; RU=11; RD=4 HLKFNMHAD SOPUMNSZW EIHCKJEXA PLMRJKPWT DAHMNFKLH WZSNMUPOS AXEJKCHIE TWPKJRMLP
LU=2; LD=1; RU=11; RD=4 HMKENLFBB SNPVMOUYY EJHBKICYY PKMSJLRVV BBFLNEKMH YYUOMVPNS YYCIKBHJE VVRLJSMKP
LU=4; LD=11; RU=1; RD=2 DEAMPLXDV WVZNKOCWE ABXJMIUAS TSWKHLZTB VDXLPMAED EWCOKNZVW SAUIMJXBA BTZLHKWST
LU=11; LD=4; RU=1; RD=2 DLAFPEJKH WOZUKVQPS AIXCMBGHE TLWRHSNMP HKJEPFALD SPQVKUZOW EHGBMCXIA PMNSHRWLT
LU=4; LD=11; RU=2; RD=1 BFBLQMWDV YUYOJNDWE YCYINJTAS VRVLGKATB VDWMQLBFB EWDNJOYUY SATJNIYCY BTAKGLVRV
LU=11; LD=4; RU=2; RD=1 BMBEQFIKH YNYVJURPS YJYBNCFHE VKVSGROMP HKIFQEBMB SPRUJVYNY EHFCNBYJY PMORGSVKV
1,2,4,12 LU=1; LD=2; RU=4; RD=12 XEDNGFPAD CVWMTUKZW UBAKDCMXA ZSTJQRHWT DAPFGNDEX WZKUTMWVC AXMCDKABU TWHRQJTSZ
LU=2; LD=1; RU=4; RD=12 XFDMGENBB CUWNTVMYY UCAJDBKYY ZRTKQSJVV BBNEGMDFX YYMVTNWUC YYKBDJACU VVJSQKTRZ
LU=1; LD=2; RU=12; RD=4 HMLFONHAD SNOULMSZW EJICLKEXA PKLRIJPWT DAHNOFLMH WZSMLUONS AXEKLCIJE TWPJIRLKP
LU=2; LD=1; RU=12; RD=4 HNLEOMFBB SMOVLNUYY EKIBLJCYY PJLSIKRVV BBFMOELNH YYUNLVOMS YYCJLBIKE VVRKISLJP
LU=4; LD=12; RU=1; RD=2 DEANQMZDX WVZMJNAWC ABXKNJWAU TSWJGKXTZ XDZMQNAED CWANJMZVW UAWJNKXBA ZTXKGJWST
LU=12; LD=4; RU=1; RD=2 DMAFQEJLH WNZUJVQOS AJXCNBGIE TKWRGSNLP HLJEQFAMD SOQVJUZNW EIGBNCXJA PLNSGRWKT
LU=4; LD=12; RU=2; RD=1 BFBMRNYDX YUYNIMBWC YCYJOKVAU VRVKFJYTZ XDYNRMBFB CWBMINYUY UAVKOJYCY ZTYJFKVRV
LU=12; LD=4; RU=2; RD=1 BNBERFILH YMYVIUROS YKYBOCFIE VJVSFROLP HLIFREBNB SORUIVYMY EIFCOBYKY PLORFSVJV
1,2,4,13 LU=1; LD=2; RU=4; RD=13 ZEDOGFQAD AVWLTUJZW WBALDCNXA XSTIQRGWT DAQFGODEZ WZJUTLWVA AXNCDLABW TWGRQITSX
LU=2; LD=1; RU=4; RD=13 ZFDNGEOBB AUWMTVLYY WCAKDBLYY XRTJQSIVV BBOEGNDFZ YYLVTMWUA YYLBDKACW VVISQJTRX
LU=1; LD=2; RU=13; RD=4 HNMFPOHAD SMNUKLSZW EKJCMLEXA PJKRHIPWT DAHOPFMNH WZSLKUNMS AXELMCJKE TWPIHRKJP
LU=2; LD=1; RU=13; RD=4 HOMEPNFBB SLNVKMUYY ELJBMKCYY PIKSHJRVV BBFNPEMOH YYUMKVNLS YYCKMBJLE VVRJHSKIP
LU=4; LD=13; RU=1; RD=2 DEAORN*DZ WVZLIM*WA ABXLOK*AW TSWIFJ*TX ZD*NROAED AW*MILZVW WA*KOLXBA XT*JFIWST ERROR
LU=13; LD=4; RU=1; RD=2 DNAFREJMH WMZUIVQNS AKXCOBGJE TJWRFSNKP HMJERFAND SNQVIUZMW EJGBOCXKA PKNSFRWJT
LU=4; LD=13; RU=2; RD=1 BFBNSO*DZ YUYMHL*WA YCYKPL*AW VRVJEI*TX ZD*OSNBFB AW*LHMYUY WA*LPKYCY XT*IEJVRV ERROR
LU=13; LD=4; RU=2; RD=1 BOBESFIMH YLYVHURNS YLYBPCFJE VIVSEROKP HMIFSEBOB SNRUHVYLY EJFCPBYLY PKORESVIV
1,2,5,10 LU=1; LD=2; RU=5; RD=10 TFELHGNAD GUVOSTMZW QCBIEDKXA DRSLPQJWT DANGHLEFT WZMTSOVUG AXKDEIBCQ TWJQPLSRD
LU=2; LD=1; RU=5; RD=10 TGEKHFLBB GTVPSUOYY QDBHECIYY DQSMPRLVV BBLFHKEGT YYOUSPVTG YYICEHBDQ VVLRPMSQD
LU=1; LD=2; RU=10; RD=5 JKJGMLIAD QPQTNORZW GHGDJIFXA NMNQKLOWT DAILMGJKJ WZRONTQPQ AXFIJDGHG TWOLKQNMN
LU=2; LD=1; RU=10; RD=5 JLJFMKGBB QOQUNPTYY GIGCJHDYY NLNRKMQVV BBGKMFJLJ YYTPNUQOQ YYDHJCGIG VVQMKRNLN
LU=5; LD=10; RU=1; RD=2 DFALPKVET WUZOKPEVG ACXIMHSBQ TRWLHMBSD TEVKPLAFD GVEPKOZUW QBSHMIXCA DSBMHLWRT
LU=10; LD=5; RU=1; RD=2 DKAGPFLJJ WPZTKUOQQ AHXDMCIGG TMWQHRLNN JJLFPGAKD QQOUKTZPW GGICMDXHA NNLRHQWMT
LU=5; LD=10; RU=2; RD=1 BGBKQLUET YTYPJOFVG YDYHNIRBQ VQVMGLCSD TEULQKBGB GVFOJPYTY QBRINHYDY DSCLGMVQV
LU=10; LD=5; RU=2; RD=1 BLBFQGKJJ YOYUJTPQQ YIYCNDHGG VLVRGQMNN JJKGQFBLB QQPTJUYOY GGHDNCYIY NNMQGRVLV
1,2,5,11 LU=1; LD=2; RU=5; RD=11 VFEMHGOAD EUVNSTLZW SCBJEDLXA BRSKPQIWT DAOGHMEFV WZLTSNVUE AXLDEJBCS TWIQPKSRB
LU=2; LD=1; RU=5; RD=11 VGELHFMBB ETVOSUNYY SDBIECJYY BQSLPRKVV BBMFHLEGV YYNUSOVTE YYJCEIBDS VVKRPLSQB
LU=1; LD=2; RU=11; RD=5 JLKGNMIAD QOPTMNRZW GIHDKJFXA NLMQJKOWT DAIMNGKLJ WZRNMTPOQ AXFJKDHIG TWOKJQMLN
LU=2; LD=1; RU=11; RD=5 JMKFNLGBB QNPUMOTYY GJHCKIDYY NKMRJLQVV BBGLNFKMJ YYTOMUPNQ YYDIKCHJG VVQLJRMKN
LU=5; LD=11; RU=1; RD=2 DFAMQLXEV WUZNJOCVE ACXJNIUBS TRWKGLZSB VEXLQMAFD EVCOJNZUW SBUINJXCA BSZLGKWRT
LU=11; LD=5; RU=1; RD=2 DLAGQFLKJ WOZTJUOPQ AIXDNCIHG TLWQGRLMN JKLFQGALD QPOUJTZOW GHICNDXIA NMLRGQWLT
LU=5; LD=11; RU=2; RD=1 BGBLRMWEV YTYOINDVE YDYIOJTBS VQVLFKASB VEWMRLBGB EVDNIOYTY SBTJOIYDY BSAKFLVQV
LU=11; LD=5; RU=2; RD=1 BMBFRGKKJ YNYUITPPQ YJYCODHHG VKVRFQMMN JKKGRFBMB QPPTIUYNY GHHDOCYJY NMMQFRVKV
1,2,5,12 LU=1; LD=2; RU=5; RD=12 XFENHGPAD CUVMSTKZW UCBKEDMXA ZRSJPQHWT DAPGHNEFX WZKTSMVUC AXMDEKBCU TWHQPJSRZ
LU=2; LD=1; RU=5; RD=12 XGEMHFNBB CTVNSUMYY UDBJECKYY ZQSKPRJVV BBNFHMEGX YYMUSNVTC YYKCEJBDU VVJRPKSQZ
LU=1; LD=2; RU=12; RD=5 JMLGONIAD QNOTLMRZW GJIDLKFXA NKLQIJOWT DAINOGLMJ WZRMLTONQ AXFKLDIJG TWOJIQLKN
LU=2; LD=1; RU=12; RD=5 JNLFOMGBB QMOULNTYY GKICLJDYY NJLRIKQVV BBGMOFLNJ YYTNLUOMQ YYDJLCIKG VVQKIRLJN
LU=5; LD=12; RU=1; RD=2 DFANRMZEX WUZMINAVC ACXKOJWBU TRWJFKXSZ XEZMRNAFD CVANIMZUW UBWJOKXCA ZSXKFJWRT
LU=12; LD=5; RU=1; RD=2 DMAGRFLLJ WNZTIUOOQ AJXDOCIIG TKWQFRLLN JLLFRGAMD QOOUITZNW GIICODXJA NLLRFQWKT
LU=5; LD=12; RU=2; RD=1 BGBMSNYEX YTYNHMBVC YDYJPKVBU VQVKEJYSZ XEYNSMBGB CVBMHNYTY UBVKPJYDY ZSYJEKVQV
LU=12; LD=5; RU=2; RD=1 BNBFSGKLJ YMYUHTPOQ YKYCPDHIG VJVREQMLN JLKGSFBNB QOPTHUYMY GIHDPCYKY NLMQERVJV
1,2,5,13 LU=1; LD=2; RU=5; RD=13 ZFEOHGQAD AUVLSTJZW WCBLEDNXA XRSIPQGWT DAQGHOEFZ WZJTSLVUA AXNDELBCW TWGQPISRX
LU=2; LD=1; RU=5; RD=13 ZGENHFOBB ATVMSULYY WDBKECLYY XQSJPRIVV BBOFHNEGZ YYLUSMVTA YYLCEKBDW VVIRPJSQX
LU=1; LD=2; RU=13; RD=5 JNMGPOIAD QMNTKLRZW GKJDMLFXA NJKQHIOWT DAIOPGMNJ WZRLKTNMQ AXFLMDJKG TWOIHQKJN
LU=2; LD=1; RU=13; RD=5 JOMFPNGBB QLNUKMTYY GLJCMKDYY NIKRHJQVV BBGNPFMOJ YYTMKUNLQ YYDKMCJLG VVQJHRKIN
LU=5; LD=13; RU=1; RD=2 DFAOSN*EZ WUZLHM*VA ACXLPK*BW TRWIEJ*SX ZE*NSOAFD AV*MHLZUW WB*KPLXCA XS*JEIWRT ERROR
LU=13; LD=5; RU=1; RD=2 DNAGSFLMJ WMZTHUONQ AKXDPCIJG TJWQERLKN JMLFSGAND QNOUHTZMW GJICPDXKA NKLREQWJT
LU=5; LD=13; RU=2; RD=1 BGBNTO*EZ YTYMGL*VA YDYKQL*BW VQVJDI*SX ZE*OTNBGB AV*LGMYTY WB*LQKYDY XS*IDJVQV ERROR
LU=13; LD=5; RU=2; RD=1 BOBFTGKMJ YLYUGTPNQ YLYCQDHJG VIVRDQMKN JMKGTFBOB QNPTGUYLY GJHDQCYLY NKMQDRVIV
1,2,5,14 LU=1; LD=2; RU=5; RD=14 *FEPHGRAD *UVKSTIZW *CBMEDOXA *RSHPQFWT DARGHPEF* WZITSKVU* AXODEMBC* TWFQPHSR* ERROR
LU=2; LD=1; RU=5; RD=14 *GEOHFPBB *TVLSUKYY *DBLECMYY *QSIPRHVV BBPFHOEG* YYKUSLVT* YYMCELBD* VVHRPISQ* ERROR
LU=1; LD=2; RU=14; RD=5 JONGQPIAD QLMTJKRZW GLKDNMFXA NIJQGHOWT DAIPQGNOJ WZRKJTMLQ AXFMNDKLG TWOHGQJIN
LU=2; LD=1; RU=14; RD=5 JPNFQOGBB QKMUJLTYY GMKCNLDYY NHJRGIQVV BBGOQFNPJ YYTLJUMKQ YYDLNCKMG VVQIGRJHN
LU=5; LD=14; RU=1; RD=2 DFAPTO*E* WUZKGL*V* ACXMQL*B* TRWHDI*S* *E*OTPAFD *V*LGKZUW *B*LQMXCA *S*IDHWRT ERROR
LU=14; LD=5; RU=1; RD=2 DOAGTFLNJ WLZTGUOMQ ALXDQCIKG TIWQDRLJN JNLFTGAOD QMOUGTZLW GKICQDXLA NJLRDQWIT
LU=5; LD=14; RU=2; RD=1 BGBOUP*E* YTYLFK*V* YDYLRM*B* VQVICH*S* *E*PUOBGB *V*KFLYTY *B*MRLYDY *S*HCIVQV ERROR
LU=14; LD=5; RU=2; RD=1 BPBFUGKNJ YKYUFTPMQ YMYCRDHKG VHVRCQMJN JNKGUFBPB QMPTFUYKY GKHDRCYMY NJMQCRVHV
1,2,5,15 LU=1; LD=2; RU=5; RD=15 *FEQHGSAD *UVJSTHZW *CBNEDPXA *RSGPQEWT DASGHQEF* WZHTSJVU* AXPDENBC* TWEQPGSR* ERROR
LU=2; LD=1; RU=5; RD=15 *GEPHFQBB *TVKSUJYY *DBMECNYY *QSHPRGVV BBQFHPEG* YYJUSKVT* YYNCEMBD* VVGRPHSQ* ERROR
LU=1; LD=2; RU=15; RD=5 JPOGRQIAD QKLTIJRZW GMLDONFXA NHIQFGOWT DAIQRGOPJ WZRJITLKQ AXFNODLMG TWOGFQIHN
LU=2; LD=1; RU=15; RD=5 JQOFRPGBB QJLUIKTYY GNLCOMDYY NGIRFHQVV BBGPRFOQJ YYTKIULJQ YYDMOCLNG VVQHFRIGN
LU=5; LD=15; RU=1; RD=2 DFAQUP*E* WUZJFK*V* ACXNRM*B* TRWGCH*S* *E*PUQAFD *V*KFJZUW *B*MRNXCA *S*HCGWRT ERROR
LU=15; LD=5; RU=1; RD=2 DPAGUFLOJ WKZTFUOLQ AMXDRCILG THWQCRLIN JOLFUGAPD QLOUFTZKW GLICRDXMA NILRCQWHT
LU=5; LD=15; RU=2; RD=1 BGBPVQ*E* YTYKEJ*V* YDYMSN*B* VQVHBG*S* *E*QVPBGB *V*JEKYTY *B*NSMYDY *S*GBHVQV ERROR
LU=15; LD=5; RU=2; RD=1 BQBFVGKOJ YJYUETPLQ YNYCSDHLG VGVRBQMIN JOKGVFBQB QLPTEUYJY GLHDSCYNY NIMQBRVGV
1,3,5,10 LU=1; LD=3; RU=5; RD=10 TFEMIHPAF GUVNRSKZU QCBJFEMXC DRSKOPHWR FAPHIMEFT UZKSRNVUG CXMEFJBCQ RWHPOKSRD
LU=3; LD=1; RU=5; RD=10 THEKIFLCB GSVPRUOXY QEBHFCIZY DPSMORLUV BCLFIKEHT YXOURPVSG YZICFHBEQ VULROMSPD
LU=1; LD=3; RU=10; RD=5 JKJHNMKAF QPQSMNPZU GHGEKJHXC NMNPJKMWR FAKMNHJKJ UZPNMSQPQ CXHJKEGHG RWMKJPNMN
LU=3; LD=1; RU=10; RD=5 JMJFNKGCB QNQUMPTXY GJGCKHDZY NKNRJMQUV BCGKNFJMJ YXTPMUQNQ YZDHKCGJG VUQMJRNKN
LU=5; LD=10; RU=1; RD=3 FFAMPKWET UUZNKPDVG CCXJMHTBQ RRWKHMASD TEWKPMAFF GVDPKNZUU QBTHMJXCC DSAMHKWRR
LU=10; LD=5; RU=1; RD=3 FKAHPFMJJ UPZSKUNQQ CHXEMCJGG RMWPHRKNN JJMFPHAKF QQNUKSZPU GGJCMEXHC NNKRHPWMR
LU=5; LD=10; RU=3; RD=1 BHCKRMUET YSXPINFVG YEZHOJRBQ VPUMFKCSD TEUMRKCHB GVFNIPXSY QBRJOHZEY DSCKFMUPV
LU=10; LD=5; RU=3; RD=1 BMCFRHKJJ YNXUISPQQ YJZCOEHGG VKURFPMNN JJKHRFCMB QQPSIUXNY GGHEOCZJY NNMPFRUKV
1,3,5,11 LU=1; LD=3; RU=5; RD=11 VFENIHQAF EUVMRSJZU SCBKFENXC BRSJOPGWR FAQHINEFV UZJSRMVUE CXNEFKBCS RWGPOJSRB
LU=3; LD=1; RU=5; RD=11 VHELIFMCB ESVORUNXY SEBIFCJZY BPSLORKUV BCMFILEHV YXNUROVSE YZJCFIBES VUKROLSPB
LU=1; LD=3; RU=11; RD=5 JLKHONKAF QOPSLMPZU GIHELKHXC NLMPIJMWR FAKNOHKLJ UZPMLSPOQ CXHKLEHIG RWMJIPMLN
LU=3; LD=1; RU=11; RD=5 JNKFOLGCB QMPULOTXY GKHCLIDZY NJMRILQUV BCGLOFKNJ YXTOLUPMQ YZDILCHKG VUQLIRMJN
LU=5; LD=11; RU=1; RD=3 FFANQLYEV UUZMJOBVE CCXKNIVBS RRWJGLYSB VEYLQNAFF EVBOJMZUU SBVINKXCC BSYLGJWRR
LU=11; LD=5; RU=1; RD=3 FLAHQFMKJ UOZSJUNPQ CIXENCJHG RLWPGRKMN JKMFQHALF QPNUJSZOU GHJCNEXIC NMKRGPWLR
LU=5; LD=11; RU=3; RD=1 BHCLSNWEV YSXOHMDVE YEZIPKTBS VPULEJASB VEWNSLCHB EVDMHOXSY SBTKPIZEY BSAJELUPV
LU=11; LD=5; RU=3; RD=1 BNCFSHKKJ YMXUHSPPQ YKZCPEHHG VJUREPMMN JKKHSFCNB QPPSHUXMY GHHEPCZKY NMMPERUJV
1,3,5,12 LU=1; LD=3; RU=5; RD=12 XFEOIHRAF CUVLRSIZU UCBLFEOXC ZRSIOPFWR FARHIOEFX UZISRLVUC CXOEFLBCU RWFPOISRZ
LU=3; LD=1; RU=5; RD=12 XHEMIFNCB CSVNRUMXY UEBJFCKZY ZPSKORJUV BCNFIMEHX YXMURNVSC YZKCFJBEU VUJROKSPZ
LU=1; LD=3; RU=12; RD=5 JMLHPOKAF QNOSKLPZU GJIEMLHXC NKLPHIMWR FAKOPHLMJ UZPLKSONQ CXHLMEIJG RWMIHPLKN
LU=3; LD=1; RU=12; RD=5 JOLFPMGCB QLOUKNTXY GLICMJDZY NILRHKQUV BCGMPFLOJ YXTNKUOLQ YZDJMCILG VUQKHRLIN
LU=5; LD=12; RU=1; RD=3 FFAORM*EX UUZLIN*VC CCXLOJ*BU RRWIFK*SZ XE*MROAFF CV*NILZUU UB*JOLXCC ZS*KFIWRR ERROR
LU=12; LD=5; RU=1; RD=3 FMAHRFMLJ UNZSIUNOQ CJXEOCJIG RKWPFRKLN JLMFRHAMF QONUISZNU GIJCOEXJC NLKRFPWKR
LU=5; LD=12; RU=3; RD=1 BHCMTOYEX YSXNGLBVC YEZJQLVBU VPUKDIYSZ XEYOTMCHB CVBLGNXSY UBVLQJZEY ZSYIDKUPV
LU=12; LD=5; RU=3; RD=1 BOCFTHKLJ YLXUGSPOQ YLZCQEHIG VIURDPMLN JLKHTFCOB QOPSGUXLY GIHEQCZLY NLMPDRUIV
1,3,5,13 LU=1; LD=3; RU=5; RD=13 ZFEPIHSAF AUVKRSHZU WCBMFEPXC XRSHOPEWR FASHIPEFZ UZHSRKVUA CXPEFMBCW RWEPOHSRX
LU=3; LD=1; RU=5; RD=13 ZHENIFOCB ASVMRULXY WEBKFCLZY XPSJORIUV BCOFINEHZ YXLURMVSA YZLCFKBEW VUIROJSPX
LU=1; LD=3; RU=13; RD=5 JNMHQPKAF QMNSJKPZU GKJENMHXC NJKPGHMWR FAKPQHMNJ UZPKJSNMQ CXHMNEJKG RWMHGPKJN
LU=3; LD=1; RU=13; RD=5 JPMFQNGCB QKNUJMTXY GMJCNKDZY NHKRGJQUV BCGNQFMPJ YXTMJUNKQ YZDKNCJMG VUQJGRKHN
LU=5; LD=13; RU=1; RD=3 FFAPSN*EZ UUZKHM*VA CCXMPK*BW RRWHEJ*SX ZE*NSPAFF AV*MHKZUU WB*KPMXCC XS*JEHWRR ERROR
LU=13; LD=5; RU=1; RD=3 FNAHSFMMJ UMZSHUNNQ CKXEPCJJG RJWPERKKN JMMFSHANF QNNUHSZMU GJJCPEXKC NKKREPWJR
LU=5; LD=13; RU=3; RD=1 BHCNUP*EZ YSXMFK*VA YEZKRM*BW VPUJCH*SX ZE*PUNCHB AV*KFMXSY WB*MRKZEY XS*HCJUPV ERROR
LU=13; LD=5; RU=3; RD=1 BPCFUHKMJ YKXUFSPNQ YMZCREHJG VHURCPMKN JMKHUFCPB QNPSFUXKY GJHERCZMY NKMPCRUHV
1,3,5,14 LU=1; LD=3; RU=5; RD=14 *FEQIHTAF *UVJRSGZU *CBNFEQXC *RSGOPDWR FATHIQEF* UZGSRJVU* CXQEFNBC* RWDPOGSR* ERROR
LU=3; LD=1; RU=5; RD=14 *HEOIFPCB *SVLRUKXY *EBLFCMZY *PSIORHUV BCPFIOEH* YXKURLVS* YZMCFLBE* VUHROISP* ERROR
LU=1; LD=3; RU=14; RD=5 JONHRQKAF QLMSIJPZU GLKEONHXC NIJPFGMWR FAKQRHNOJ UZPJISMLQ CXHNOEKLG RWMGFPJIN
LU=3; LD=1; RU=14; RD=5 JQNFROGCB QJMUILTXY GNKCOLDZY NGJRFIQUV BCGORFNQJ YXTLIUMJQ YZDLOCKNG VUQIFRJGN
LU=5; LD=14; RU=1; RD=3 FFAQTO*E* UUZJGL*V* CCXNQL*B* RRWGDI*S* *E*OTQAFF *V*LGJZUU *B*LQNXCC *S*IDGWRR ERROR
LU=14; LD=5; RU=1; RD=3 FOAHTFMNJ ULZSGUNMQ CLXEQCJKG RIWPDRKJN JNMFTHAOF QMNUGSZLU GKJCQEXLC NJKRDPWIR
LU=5; LD=14; RU=3; RD=1 BHCOVQ*E* YSXLEJ*V* YEZLSN*B* VPUIBG*S* *E*QVOCHB *V*JELXSY *B*NSLZEY *S*GBIUPV ERROR
LU=14; LD=5; RU=3; RD=1 BQCFVHKNJ YJXUESPMQ YNZCSEHKG VGURBPMJN JNKHVFCQB QMPSEUXJY GKHESCZNY NJMPBRUGV
1,3,5,15 LU=1; LD=3; RU=5; RD=15 *FERIHUAF *UVIRSFZU *CBOFERXC *RSFOPCWR FAUHIREF* UZFSRIVU* CXREFOBC* RWCPOFSR* ERROR
LU=3; LD=1; RU=5; RD=15 *HEPIFQCB *SVKRUJXY *EBMFCNZY *PSHORGUV BCQFIPEH* YXJURKVS* YZNCFMBE* VUGROHSP* ERROR
LU=1; LD=3; RU=15; RD=5 JPOHSRKAF QKLSHIPZU GMLEPOHXC NHIPEFMWR FAKRSHOPJ UZPIHSLKQ CXHOPELMG RWMFEPIHN
LU=3; LD=1; RU=15; RD=5 JROFSPGCB QILUHKTXY GOLCPMDZY NFIREHQUV BCGPSFORJ YXTKHULIQ YZDMPCLOG VUQHERIFN
LU=5; LD=15; RU=1; RD=3 FFARUP*E* UUZIFK*V* CCXORM*B* RRWFCH*S* *E*PURAFF *V*KFIZUU *B*MROXCC *S*HCFWRR ERROR
LU=15; LD=5; RU=1; RD=3 FPAHUFMOJ UKZSFUNLQ CMXERCJLG RHWPCRKIN JOMFUHAPF QLNUFSZKU GLJCREXMC NIKRCPWHR
LU=5; LD=15; RU=3; RD=1 BHCPWR*E* YSXKDI*V* YEZMTO*B* VPUHAF*S* *E*RWPCHB *V*IDKXSY *B*OTMZEY *S*FAHUPV ERROR
LU=15; LD=5; RU=3; RD=1 BRCFWHKOJ YIXUDSPLQ YOZCTEHLG VFURAPMIN JOKHWFCRB QLPSDUXIY GLHETCZOY NIMPARUFV
1,3,6,12 LU=1; LD=3; RU=6; RD=12 XGFOJIRAF CTULQRIZU UDCLGFOXC ZQRINOFWR FARIJOFGX UZIRQLUTC CXOFGLCDU RWFONIRQZ
LU=3; LD=1; RU=6; RD=12 XIFMJGNCB CRUNQTMXY UFCJGDKZY ZORKNQJUV BCNGJMFIX YXMTQNURC YZKDGJCFU VUJQNKROZ
LU=1; LD=3; RU=12; RD=6 LMLIPOLAF ONORKLOZU IJIFMLIXC LKLOHILWR FALOPILML UZOLKRONO CXILMFIJI RWLIHOLKL
LU=3; LD=1; RU=12; RD=6 LOLGPMHCB OLOTKNSXY ILIDMJEZY LILQHKPUV BCHMPGLOL YXSNKTOLO YZEJMDILI VUPKHQLIL
LU=6; LD=12; RU=1; RD=3 FGAOSM*FX UTZLHN*UC CDXLPJ*CU RQWIEK*RZ XF*MSOAGF CU*NHLZTU UC*JPLXDC ZR*KEIWQR ERROR
LU=12; LD=6; RU=1; RD=3 FMAISGOLL UNZRHTLOO CJXFPDLII RKWOEQILL LLOGSIAMF OOLTHRZNU IILDPFXJC LLIQEOWKR
LU=6; LD=12; RU=3; RD=1 BICMUOYFX YRXNFLBUC YFZJRLVCU VOUKCIYRZ XFYOUMCIB CUBLFNXRY UCVLRJZFY ZRYICKUOV
LU=12; LD=6; RU=3; RD=1 BOCGUIMLL YLXTFRNOO YLZDRFJII VIUQCOKLL LLMIUGCOB OONRFTXLY IIJFRDZLY LLKOCQUIV
1,3,6,13 LU=1; LD=3; RU=6; RD=13 ZGFPJISAF ATUKQRHZU WDCMGFPXC XQRHNOEWR FASIJPFGZ UZHRQKUTA CXPFGMCDW RWEONHRQX
LU=3; LD=1; RU=6; RD=13 ZIFNJGOCB ARUMQTLXY WFCKGDLZY XORJNQIUV BCOGJNFIZ YXLTQMURA YZLDGKCFW VUIQNJROX
LU=1; LD=3; RU=13; RD=6 LNMIQPLAF OMNRJKOZU IKJFNMIXC LJKOGHLWR FALPQIMNL UZOKJRNMO CXIMNFJKI RWLHGOKJL
LU=3; LD=1; RU=13; RD=6 LPMGQNHCB OKNTJMSXY IMJDNKEZY LHKQGJPUV BCHNQGMPL YXSMJTNKO YZEKNDJMI VUPJGQKHL
LU=6; LD=13; RU=1; RD=3 FGAPTN*FZ UTZKGM*UA CDXMQK*CW RQWHDJ*RX ZF*NTPAGF AU*MGKZTU WC*KQMXDC XR*JDHWQR ERROR
LU=13; LD=6; RU=1; RD=3 FNAITGOML UMZRGTLNO CKXFQDLJI RJWODQIKL LMOGTIANF ONLTGRZMU IJLDQFXKC LKIQDOWJR
LU=6; LD=13; RU=3; RD=1 BICNVP*FZ YRXMEK*UA YFZKSM*CW VOUJBH*RX ZF*PVNCIB AU*KEMXRY WC*MSKZFY XR*HBJUOV ERROR
LU=13; LD=6; RU=3; RD=1 BPCGVIMML YKXTERNNO YMZDSFJJI VHUQBOKKL LMMIVGCPB ONNRETXKY IJJFSDZMY LKKOBQUHV
1,3,6,14 LU=1; LD=3; RU=6; RD=14 *GFQJITAF *TUJQRGZU *DCNGFQXC *QRGNODWR FATIJQFG* UZGRQJUT* CXQFGNCD* RWDONGRQ* ERROR
LU=3; LD=1; RU=6; RD=14 *IFOJGPCB *RULQTKXY *FCLGDMZY *ORINQHUV BCPGJOFI* YXKTQLUR* YZMDGLCF* VUHQNIRO* ERROR
LU=1; LD=3; RU=14; RD=6 LONIRQLAF OLMRIJOZU ILKFONIXC LIJOFGLWR FALQRINOL UZOJIRMLO CXINOFKLI RWLGFOJIL
LU=3; LD=1; RU=14; RD=6 LQNGROHCB OJMTILSXY INKDOLEZY LGJQFIPUV BCHORGNQL YXSLITMJO YZELODKNI VUPIFQJGL
LU=6; LD=14; RU=1; RD=3 FGAQUO*F* UTZJFL*U* CDXNRL*C* RQWGCI*R* *F*OUQAGF *U*LFJZTU *C*LRNXDC *R*ICGWQR ERROR
LU=14; LD=6; RU=1; RD=3 FOAIUGONL ULZRFTLMO CLXFRDLKI RIWOCQIJL LNOGUIAOF OMLTFRZLU IKLDRFXLC LJIQCOWIR
LU=6; LD=14; RU=3; RD=1 BICOWQ*F* YRXLDJ*U* YFZLTN*C* VOUIAG*R* *F*QWOCIB *U*JDLXRY *C*NTLZFY *R*GAIUOV ERROR
LU=14; LD=6; RU=3; RD=1 BQCGWIMNL YJXTDRNMO YNZDTFJKI VGUQAOKJL LNMIWGCQB OMNRDTXJY IKJFTDZNY LJKOAQUGV
1,3,6,15 LU=1; LD=3; RU=6; RD=15 *GFRJIUAF *TUIQRFZU *DCOGFRXC *QRFNOCWR FAUIJRFG* UZFRQIUT* CXRFGOCD* RWCONFRQ* ERROR
LU=3; LD=1; RU=6; RD=15 *IFPJGQCB *RUKQTJXY *FCMGDNZY *ORHNQGUV BCQGJPFI* YXJTQKUR* YZNDGMCF* VUGQNHRO* ERROR
LU=1; LD=3; RU=15; RD=6 LPOISRLAF OKLRHIOZU IMLFPOIXC LHIOEFLWR FALRSIOPL UZOIHRLKO CXIOPFLMI RWLFEOIHL
LU=3; LD=1; RU=15; RD=6 LROGSPHCB OILTHKSXY IOLDPMEZY LFIQEHPUV BCHPSGORL YXSKHTLIO YZEMPDLOI VUPHEQIFL
LU=6; LD=15; RU=1; RD=3 FGARVP*F* UTZIEK*U* CDXOSM*C* RQWFBH*R* *F*PVRAGF *U*KEIZTU *C*MSOXDC *R*HBFWQR ERROR
LU=15; LD=6; RU=1; RD=3 FPAIVGOOL UKZRETLLO CMXFSDLLI RHWOBQIIL LOOGVIAPF OLLTERZKU ILLDSFXMC LIIQBOWHR
LU=6; LD=15; RU=3; RD=1 BICPXR*F* YRXKCI*U* YFZMUO*C* VOUHZF*R* *F*RXPCIB *U*ICKXRY *C*OUMZFY *R*FZHUOV ERROR
LU=15; LD=6; RU=3; RD=1 BRCGXIMOL YIXTCRNLO YOZDUFJLI VFUQZOKIL LOMIXGCRB OLNRCTXIY ILJFUDZOY LIKOZQUFV
1,3,6,16 LU=1; LD=3; RU=6; RD=16 *GFSJIVAF *TUHQREZU *DCPGFSXC *QRENOBWR FAVIJSFG* UZERQHUT* CXSFGPCD* RWBONERQ* ERROR
LU=3; LD=1; RU=6; RD=16 *IFQJGRCB *RUJQTIXY *FCNGDOZY *ORGNQFUV BCRGJQFI* YXITQJUR* YZODGNCF* VUFQNGRO* ERROR
LU=1; LD=3; RU=16; RD=6 LQPITSLAF OJKRGHOZU INMFQPIXC LGHODELWR FALSTIPQL UZOHGRKJO CXIPQFMNI RWLEDOHGL
LU=3; LD=1; RU=16; RD=6 LSPGTQHCB OHKTGJSXY IPMDQNEZY LEHQDGPUV BCHQTGPSL YXSJGTKHO YZENQDMPI VUPGDQHEL
LU=6; LD=16; RU=1; RD=3 FGASWQ*F* UTZHDJ*U* CDXPTN*C* RQWEAG*R* *F*QWSAGF *U*JDHZTU *C*NTPXDC *R*GAEWQR ERROR
LU=16; LD=6; RU=1; RD=3 FQAIWGOPL UJZRDTLKO CNXFTDLMI RGWOAQIHL LPOGWIAQF OKLTDRZJU IMLDTFXNC LHIQAOWGR
LU=6; LD=16; RU=3; RD=1 BICQYS*F* YRXJBH*U* YFZNVP*C* VOUGYE*R* *F*SYQCIB *U*HBJXRY *C*PVNZFY *R*EYGUOV ERROR
LU=16; LD=6; RU=3; RD=1 BSCGYIMPL YHXTBRNKO YPZDVFJMI VEUQYOKHL LPMIYGCSB OKNRBTXHY IMJFVDZPY LHKOYQUEV
1,3,6,17 LU=1; LD=3; RU=6; RD=17 *GFTJIWAF *TUGQRDZU *DCQGFTXC *QRDNOAWR FAWIJTFG* UZDRQGUT* CXTFGQCD* RWAONDRQ* ERROR
LU=3; LD=1; RU=6; RD=17 *IFRJGSCB *RUIQTHXY *FCOGDPZY *ORFNQEUV BCSGJRFI* YXHTQIUR* YZPDGOCF* VUEQNFRO* ERROR
LU=1; LD=3; RU=17; RD=6 LRQIUTLAF OIJRFGOZU IONFRQIXC LFGOCDLWR FALTUIQRL UZOGFRJIO CXIQRFNOI RWLDCOGFL
LU=3; LD=1; RU=17; RD=6 LTQGURHCB OGJTFISXY IQNDROEZY LDGQCFPUV BCHRUGQTL YXSIFTJGO YZEORDNQI VUPFCQGDL
LU=6; LD=17; RU=1; RD=3 FGATXR*F* UTZGCI*U* CDXQUO*C* RQWDZF*R* *F*RXTAGF *U*ICGZTU *C*OUQXDC *R*FZDWQR ERROR
LU=17; LD=6; RU=1; RD=3 FRAIXGOQL UIZRCTLJO COXFUDLNI RFWOZQIGL LQOGXIARF OJLTCRZIU INLDUFXOC LGIQZOWFR
LU=6; LD=17; RU=3; RD=1 BICRZT*F* YRXIAG*U* YFZOWQ*C* VOUFXD*R* *F*TZRCIB *U*GAIXRY *C*QWOZFY *R*DXFUOV ERROR
LU=17; LD=6; RU=3; RD=1 BTCGZIMQL YGXTARNJO YQZDWFJNI VDUQXOKGL LQMIZGCTB OJNRATXGY INJFWDZQY LGKOXQUDV
1,3,7,14 LU=1; LD=3; RU=7; RD=14 *HGQKJTAF *STJPQGZU *EDNHGQXC *PQGMNDWR FATJKQGH* UZGQPJTS* CXQGHNDE* RWDNMGQP* ERROR
LU=3; LD=1; RU=7; RD=14 *JGOKHPCB *QTLPSKXY *GDLHEMZY *NQIMPHUV BCPHKOGJ* YXKSPLTQ* YZMEHLDG* VUHPMIQN* ERROR
LU=1; LD=3; RU=14; RD=7 NONJRQMAF MLMQIJNZU KLKGONJXC JIJNFGKWR FAMQRJNON UZNJIQMLM CXJNOGKLK RWKGFNJIJ
LU=3; LD=1; RU=14; RD=7 NQNHROICB MJMSILRXY KNKEOLFZY JGJPFIOUV BCIORHNQN YXRLISMJM YZFLOEKNK VUOIFPJGJ
LU=7; LD=14; RU=1; RD=3 FHAQVO*G* USZJEL*T* CEXNSL*D* RPWGBI*Q* *G*OVQAHF *T*LEJZSU *D*LSNXEC *Q*IBGWPR ERROR
LU=14; LD=7; RU=1; RD=3 FOAJVHQNN ULZQESJMM CLXGSENKK RIWNBPGJJ NNQHVJAOF MMJSEQZLU KKNESGXLC JJGPBNWIR
LU=7; LD=14; RU=3; RD=1 BJCOXQ*G* YQXLCJ*T* YGZLUN*D* VNUIZG*Q* *G*QXOCJB *T*JCLXQY *D*NULZGY *Q*GZIUNV ERROR
LU=14; LD=7; RU=3; RD=1 BQCHXJONN YJXSCQLMM YNZEUGLKK VGUPZNIJJ NNOJXHCQB MMLQCSXJY KKLGUEZNY JJINZPUGV
1,3,7,15 LU=1; LD=3; RU=7; RD=15 *HGRKJUAF *STIPQFZU *EDOHGRXC *PQFMNCWR FAUJKRGH* UZFQPITS* CXRGHODE* RWCNMFQP* ERROR
LU=3; LD=1; RU=7; RD=15 *JGPKHQCB *QTKPSJXY *GDMHENZY *NQHMPGUV BCQHKPGJ* YXJSPKTQ* YZNEHMDG* VUGPMHQN* ERROR
LU=1; LD=3; RU=15; RD=7 NPOJSRMAF MKLQHINZU KMLGPOJXC JHINEFKWR FAMRSJOPN UZNIHQLKM CXJOPGLMK RWKFENIHJ
LU=3; LD=1; RU=15; RD=7 NROHSPICB MILSHKRXY KOLEPMFZY JFIPEHOUV BCIPSHORN YXRKHSLIM YZFMPELOK VUOHEPIFJ
LU=7; LD=15; RU=1; RD=3 FHARWP*G* USZIDK*T* CEXOTM*D* RPWFAH*Q* *G*PWRAHF *T*KDIZSU *D*MTOXEC *Q*HAFWPR ERROR
LU=15; LD=7; RU=1; RD=3 FPAJWHQON UKZQDSJLM CMXGTENLK RHWNAPGIJ NOQHWJAPF MLJSDQZKU KLNETGXMC JIGPANWHR
LU=7; LD=15; RU=3; RD=1 BJCPYR*G* YQXKBI*T* YGZMVO*D* VNUHYF*Q* *G*RYPCJB *T*IBKXQY *D*OVMZGY *Q*FYHUNV ERROR
LU=15; LD=7; RU=3; RD=1 BRCHYJOON YIXSBQLLM YOZEVGLLK VFUPYNIIJ NOOJYHCRB MLLQBSXIY KLLGVEZOY JIINYPUFV
1,3,7,16 LU=1; LD=3; RU=7; RD=16 *HGSKJVAF *STHPQEZU *EDPHGSXC *PQEMNBWR FAVJKSGH* UZEQPHTS* CXSGHPDE* RWBNMEQP* ERROR
LU=3; LD=1; RU=7; RD=16 *JGQKHRCB *QTJPSIXY *GDNHEOZY *NQGMPFUV BCRHKQGJ* YXISPJTQ* YZOEHNDG* VUFPMGQN* ERROR
LU=1; LD=3; RU=16; RD=7 NQPJTSMAF MJKQGHNZU KNMGQPJXC JGHNDEKWR FAMSTJPQN UZNHGQKJM CXJPQGMNK RWKEDNHGJ
LU=3; LD=1; RU=16; RD=7 NSPHTQICB MHKSGJRXY KPMEQNFZY JEHPDGOUV BCIQTHPSN YXRJGSKHM YZFNQEMPK VUOGDPHEJ
LU=7; LD=16; RU=1; RD=3 FHASXQ*G* USZHCJ*T* CEXPUN*D* RPWEZG*Q* *G*QXSAHF *T*JCHZSU *D*NUPXEC *Q*GZEWPR ERROR
LU=16; LD=7; RU=1; RD=3 FQAJXHQPN UJZQCSJKM CNXGUENMK RGWNZPGHJ NPQHXJAQF MKJSCQZJU KMNEUGXNC JHGPZNWGR
LU=7; LD=16; RU=3; RD=1 BJCQZS*G* YQXJAH*T* YGZNWP*D* VNUGXE*Q* *G*SZQCJB *T*HAJXQY *D*PWNZGY *Q*EXGUNV ERROR
LU=16; LD=7; RU=3; RD=1 BSCHZJOPN YHXSAQLKM YPZEWGLMK VEUPXNIHJ NPOJZHCSB MKLQASXHY KMLGWEZPY JHINXPUEV
1,3,7,17 LU=1; LD=3; RU=7; RD=17 *HGTKJWAF *STGPQDZU *EDQHGTXC *PQDMNAWR FAWJKTGH* UZDQPGTS* CXTGHQDE* RWANMDQP* ERROR
LU=3; LD=1; RU=7; RD=17 *JGRKHSCB *QTIPSHXY *GDOHEPZY *NQFMPEUV BCSHKRGJ* YXHSPITQ* YZPEHODG* VUEPMFQN* ERROR
LU=1; LD=3; RU=17; RD=7 NRQJUTMAF MIJQFGNZU KONGRQJXC JFGNCDKWR FAMTUJQRN UZNGFQJIM CXJQRGNOK RWKDCNGFJ
LU=3; LD=1; RU=17; RD=7 NTQHURICB MGJSFIRXY KQNEROFZY JDGPCFOUV BCIRUHQTN YXRIFSJGM YZFORENQK VUOFCPGDJ
LU=7; LD=17; RU=1; RD=3 FHATYR*G* USZGBI*T* CEXQVO*D* RPWDYF*Q* *G*RYTAHF *T*IBGZSU *D*OVQXEC *Q*FYDWPR ERROR
LU=17; LD=7; RU=1; RD=3 FRAJYHQQN UIZQBSJJM COXGVENNK RFWNYPGGJ NQQHYJARF MJJSBQZIU KNNEVGXOC JGGPYNWFR
LU=7; LD=17; RU=3; RD=1 BJCR*T*G* YQXI*G*T* YGZO*Q*D* VNUF*D*Q* *G*T*RCJB *T*G*IXQY *D*Q*OZGY *Q*D*FUNV ERROR
LU=17; LD=7; RU=3; RD=1 BTCH*JOQN YGXS*QLJM YQZE*GLNK VDUP*NIGJ NQOJ*HCTB MJLQ*SXGY KNLG*EZQY JGIN*PUDV ERROR
1,3,7,18 LU=1; LD=3; RU=7; RD=18 *HGUKJXAF *STFPQCZU *EDRHGUXC *PQCMNZWR FAXJKUGH* UZCQPFTS* CXUGHRDE* RWZNMCQP* ERROR
LU=3; LD=1; RU=7; RD=18 *JGSKHTCB *QTHPSGXY *GDPHEQZY *NQEMPDUV BCTHKSGJ* YXGSPHTQ* YZQEHPDG* VUDPMEQN* ERROR
LU=1; LD=3; RU=18; RD=7 NSRJVUMAF MHIQEFNZU KPOGSRJXC JEFNBCKWR FAMUVJRSN UZNFEQIHM CXJRSGOPK RWKCBNFEJ
LU=3; LD=1; RU=18; RD=7 NURHVSICB MFISEHRXY KROESPFZY JCFPBEOUV BCISVHRUN YXRHESIFM YZFPSEORK VUOEBPFCJ
LU=7; LD=18; RU=1; RD=3 FHAUZS*G* USZFAH*T* CEXRWP*D* RPWCXE*Q* *G*SZUAHF *T*HAFZSU *D*PWRXEC *Q*EXCWPR ERROR
LU=18; LD=7; RU=1; RD=3 FSAJZHQRN UHZQASJIM CPXGWENOK REWNXPGFJ NRQHZJASF MIJSAQZHU KONEWGXPC JFGPXNWER
LU=7; LD=18; RU=3; RD=1 BJCS*U*G* YQXH*F*T* YGZP*R*D* VNUE*C*Q* *G*U*SCJB *T*F*HXQY *D*R*PZGY *Q*C*EUNV ERROR
LU=18; LD=7; RU=3; RD=1 BUCH*JORN YFXS*QLIM YRZE*GLOK VCUP*NIFJ NROJ*HCUB MILQ*SXFY KOLG*EZRY JFIN*PUCV ERROR
1,3,7,19 LU=1; LD=3; RU=7; RD=19 *HGVKJYAF *STEPQBZU *EDSHGVXC *PQBMNYWR FAYJKVGH* UZBQPETS* CXVGHSDE* RWYNMBQP* ERROR
LU=3; LD=1; RU=7; RD=19 *JGTKHUCB *QTGPSFXY *GDQHERZY *NQDMPCUV BCUHKTGJ* YXFSPGTQ* YZREHQDG* VUCPMDQN* ERROR
LU=1; LD=3; RU=19; RD=7 NTSJWVMAF MGHQDENZU KQPGTSJXC JDENABKWR FAMVWJSTN UZNEDQHGM CXJSTGPQK RWKBANEDJ
LU=3; LD=1; RU=19; RD=7 NVSHWTICB MEHSDGRXY KSPETQFZY JBEPADOUV BCITWHSVN YXRGDSHEM YZFQTEPSK VUODAPEBJ
LU=7; LD=19; RU=1; RD=3 FHAV*T*G* USZE*G*T* CEXS*Q*D* RPWB*D*Q* *G*T*VAHF *T*G*EZSU *D*Q*SXEC *Q*D*BWPR ERROR
LU=19; LD=7; RU=1; RD=3 FTAJ*HQSN UGZQ*SJHM CQXG*ENPK RDWN*PGEJ NSQH*JATF MHJS*QZGU KPNE*GXQC JEGP*NWDR ERROR
LU=7; LD=19; RU=3; RD=1 BJCT*V*G* YQXG*E*T* YGZQ*S*D* VNUD*B*Q* *G*V*TCJB *T*E*GXQY *D*S*QZGY *Q*B*DUNV ERROR
LU=19; LD=7; RU=3; RD=1 BVCH*JOSN YEXS*QLHM YSZE*GLPK VBUP*NIEJ NSOJ*HCVB MHLQ*SXEY KPLG*EZSY JEIN*PUBV ERROR


Wednesday, July 27, 2016

Brach Cipher Rabbit Hole

This relates to what is (likely) the last clue for #cipherhunt

Clue says "written in the trees", combined with the "where it all began" leads many to think the first clue may have something hidden in the area where there are trees (see below):

The first thing I thought it could be was a branch cipher, but the traditional rules for a branch cipher require at least one branch on each side of the center.

I still wanted to continue down the line of assuming each tree was a character and the branches (through some combination of placement [left vs right and order], count [number of limbs], and/or direction [pointing up or down]) indicated a certain character.

Assuming each tree is a character, they only way a cryptogram solver will work on such a short cryptogram is if at least a couple of the letters are the same (there are way too many solutions for the cryptogram ABCDEFGHI [and ABCDE FGHI, if you count the gap in the middle as a space), and on the flip side, there needs to be enough diversity (AAABABBBA or any other combination of A and B is NOT a very meaningful cryptogram).

Idea 1: Use the normal rules for branch ciphers to see which trees are similar characters. Tree 1 would be 0-2 (zero branches on the left, two on the right); for the whole thing: {0-2, 1-1, 0-1, 1-1,2-1,1-1,2-1,1-0,2-0,}  or when simplified to normal cryptogram: ABCBDBDEF, which is not a useful one word cipher because no 9-letter-words (according to quipqiup) match that pattern, conversely, ABCBD BDEF (with a space to match the gap in the trees) results in way to many possible results (including my favorite: "COLON ONES").

Idea 2: same as 1, but count number of upward pointing and downward pointing branches. {2-0,0-2,0-1,2-0,1-2,1-1,3-0,0-1,2-0} or ABCADEFCA. This results in some interesting, but likely not meaningful results:

1
-2.529
EXTENUATE
2
-2.793
ERNESTINE
3
-4.104
SWASTIKAS

That last one is a little bit concerning...  With the space added, (ABCAD EFCA), we again get too many possibilities, including my favorite "THATS BOAT"

After trying some other ideas, I have come up empty. Giving up for now on finding a cipher in the trees. If there is a code where each tree is a character, then it looks like each tree is a different character, meaning it can't be solved by normal cryptogram solving and will need an external key. Hopefully this post might inspire someone to try a different, more successful approach.

Update: Since no one else has found anything in the past 14 hours, thought I would revisit this with a slight difference: treat Bill as a tree. He's obviously between the 5th and 6th tree, and has one branch arm) out. So we will just add a character into the cryptogram we made for ideas 1 and 2 and see if we get a meaningful 10 letter word.

Idea 1 becomes ABCBDEBDEF, and  quipqiup tells me that the only word it could be is "CHIHUAHUAS"

Idea 2 becomes  ABCADCEFCA which seems to have no possible one-word matches.