solution to 2020 #6

2020/6A/ciphertext.txt

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+FXWCR SURSR NJCDL IRZGV MRYJS HJEVH FXYZQ LWRWT OZVVN EDWVD XNLYY DQRUL VJJIP FESTG XQRWN FQZJL SXWMV FTMHW FILFR IKXWE GFPWT MLXZW FEXRS HWFIM FXXVV FEGKC DYJNS FZSKR GVRHT XUZHI SBKFU JZJSI HXZGJ EWXZQ RFVYT DXVVY YHWVZ FJQTK KNEJY FUJGR WKZMZ FMZVS FWFIH FCVZI SWZVJ RVABV LIRZG KFUDQ IHFUB AVWYV GFCRY FIYYH RRQIW RZEGS FWMZQ LKRWV STIWY YHGIH FBWMI RZXKH RPJNK JERSV RKKKJ CDSUO FULJJ PJEWN FQJUW MRWXY HBRVX RGYFV JVKJI SWVYN FXXIH XZGJE WQVDA VVTJX IUHSC BGLWL CDIKK FKWMV BMRGG VHSRE QVWTI HHFPR VQIJX HYDSZ FJIHU CDHVP JEWKF UYYHK CDYZP NXKYY DAVPN JVJUW MVLRG RWKDS THTWW MZVGL WBVKJ RUIKK JJDRV VYFUD RWYYU JVGNW IJIHS KDIUU JJVJJ LSKKJ VDXKH SURKC RSURS ROQNL YYWMV VFDHI VSFIW ZIHIR WJRQI KKFKF TZQHZ GJUZN KKYYH TILLZ QFCDW ILARO TWWMV VUPFQ ZVYKR ZILSX JWFXU WUTDQ TIITC NTEHT WWMVO FEGQR GNVVM RGXFP JNKFK ITIWZ ZWTLV QPNJG WFIHH FUIFI YYHHF PNEJX RQIXR NEJXF IMVUW VVNUH SKVFE GBRVF SOJKR IVVHI LGVYN JLYFU XKRYY HIVSF IWJUW JEDSK WMVUJ YDISH JEDSZ QHIHF JHNEW MVQZD EJIRA VUYYH YYUJV ZJVNX CHFUL SXXUK RYYHN IGJGD WKXWV DSUWM RWIRW JTRNE FNUHI NLYYW MVDWI LAROT WWMVV UPFQZ VYKRZ ILSXJ WFXUZ QYYHZ BLHZU HLOFK HIUHX TUNGW NFQXF IYYHI VSFIW JUWJE DSKVY FRZID LVQYJ DYKKJ GRWKD ZKKTI LYZHX RQIKK JPZJI HFSOJ KRHFQ KZURK KFKDL IRZGP FKFMZ QLKKJ UHXTU NGWNF QMRGQ VIYKK JTRZE WWPWM VGFPD KKHWK KJJSD TONJW LIRZG DWILA VGFKN NEJXT UTJVT LUFXH SKVFE GFBHQ RJWFX UJLSV VXVAF EGPVQ YNHWV DXBHI KRWVS TIWTE WMVVU PFQZV YXUTL SXZQY YHNIQ JZJMS RZIKT FGXRQ ISRYY WJRPX JHSKP JRONJ WTWWM VWTLU NEJUR UYZHX IHHFQ HZONE JYYHR RJFZQ XKWMV SFIWD FIYNH SKBYY DYJHY FIKWU TDONE FTCQB VKFMH QFVYR QTKKJ IINMH FCRSX WMVZF POZTN NCBYY HFBHQ RJWFX UZQJJ VJOKF UEJVQ BRWHY LSXIT IWMVG JGDWK XWVIW FPYYH JRVYV QIRQI JRBVN SFZYY DYKKJ WXQCW BVQYP VJKRK WDQFQ LKKJK KFDHX ZQYNR LIRZG VTWWJ EZNKK JZJMK DWILA ZQLZQ XNDQV DSUVJ MHSRW HRQJN GTEWM VDHIR XKLHZ QYYHQ RVYKH QVJWR PBVLS KHWTH UKHIJ SJCOJ URZKW MVPJJ VFXHF KWFIJ JKUIW DSULW RQYYD YGDXK PDRLW DLSZV YIBHF QYRFY JZMFD YCDXK DLIHJ UWTSU NVIRV RSKKJ ZUHFQ HVUSJ UIWVY RQIJI TIUFU LTULW VFYZR SRQIW LSULS XLVLH XKLTE HIKKN JWMZQ PZQLZ WBRVF EHWIR WRQIK KFKWM VBRVD SKUFU LTULW VFYZR SWLSU LSXWM VQFML LRWNF QXPVY VPBVX XVEZK DUGDW VQYCB YYLXZ VXFPJ KKNEJ SVZKI RRKKJ SRKWL SJRSK KJKLE RUITR RDLYK HJKKJ PFFCO NKFMR LSYRR VDSUL YIHKV UXKRF EHBRH WFSQR QJUHY VFYZR SJBXK HRKKF KXXVV WVIQV FYZRS FIWRG NFZFM HXKRW RQLVI NEGFJ ZJCOF JLSUL HRWJS HFILS XIWFP FZUYY UJRWX KKJPK FMHGV HSVAU VUNDH SKLSX ZNKKY YLXWR WRZMZ OJRQI RUJER BSXNC GNEJT LWFJH WZHXF IRRVY JWTXL AVIWF QYCLS VZFIQ NEJTW DNIDY KDHBV YYHKZ UXKIJ NVYRW NFQXR UJSHN EJGLL QKLSE RWWRQ BONEF TCQFE GJJVJ OWTGU TMLIV DWZQL FIIVI JEFJR UTLQI CRSUR SRQIZ WQFRP JONBH TLUXG BHCLX KIWZH SUVFI HMLQY ZQLWR WZQKF URRWN FQFSR ZKWMZ VYVFM ERQFJ DZWNJ QTKFQ VDWZI YYHDB QTNZM RWNKL XSXYZ WNJFJ IWFZQ YYDYN HMRYJ KRXKR UKKJD INEGN EJTLW NRPFC VTERY JXWVZ MRWYY HRZVX ZQLGD WKBRV PGVUX RUJUR NEJNK FFEWG VMZJW RFUJJ SDZQL RVYYH NIFTM HWNLY YWMVW TLUNE JURUY ZHXRO QFZJU WMVPF JPZTK FTFJJ VFJWM VBBVU JCLPV ODKRL VWXFV TDHYY LSXHQ JHNJX UZDRY RUZQL KKFKW MVDYK DHYHI ZQYVU HVSYN LQCJN MHZJD HCXJN HFEDQ PVJUW MVHST UDGWJ UWJCH LIDRR QIWRZ EGYYD YZWZJ HXRFQ RVXZF FUILM AHZSM VUNKX XVVYY HXRPJ BHDNR WUITI WMVWW RQXGR XZWNF QXKDL VRKKK JTLUY HWRVN YDAVX XVGKF UYYLX MLLVQ JIHHZ SMVUF EGPER BZQLK KFKLY JKTLO ISHWV DXFQF SODJW WRLLY WKFUB RUIKR HIDHB WMVLW DHXJD LVEZK BTLZN COMRY JKRHY HHBWM VGJKD NCVKF UDFXW JHQWD XZKFM HYFJT YDWIB MRVFJ NJUPJ KRYID AVOYF FFZVY FUYFV JKXUR FTDPF EGUFV YRWYY HWUIY FZJIL STDXV ZJEHJ UWTRF YHXNT NQPLK NHHRQ HIDHB WMZVT EHFEG BFUPF XYNKF KLXXR NEJTE WMVQN YRUVZ JTDSD RZEWF TRZEW JIWTK KJJSD TONJW TGHWR WNFQG VITIH NKVZT FJVGX GHFIO

2020/6A/plaintext.txt

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+Our London Akela groups have been scouting for clues in areas with a large German population, using the cover of Good Turn Day to visit a number of houses and flats known to be occupied by foreign residents. In most cases there was nothing to report, which is not a real surprise as VK's group had already vetted a lot of them and found nothing to report. The breakthrough came when one of the landladies mentioned that she was sad to see her previous resident leave so suddenly, but glad that they had been able to recommend such a nice replacement for the flat. I might have missed the importance of this, but we heard the same story at three different addresses in the East End of London, all with the same departure date, and that coincided with the original arrival of the spyclist touring group from Norfolk. One of the landladies had, somewhat fortuitously, kept a record of the comings and goings of her residents and was able to describe visitors to the departed tenant. There had been an increase in the number over the three weeks leading up to their departure, and that date coincided with the arrival of the spyclist touring group in the UK. I circulated descriptions of the departed tenants to our agents at the port authorities and they were able to confirm that a group matching the description had left the country the day after the spyclist group arrived at Kings Cross. Our agents and Akela groups in Essex and Kent were asked to report on the spyclist groups in their neighbourhoods, and both teams sent me a list of the touring parties. Reconciling them against the party of twenty that set off from Lincoln we have lost another five along the way. Luckily the Akela group in Essex had been watching for the departure from the East End and so we know that the full twenty set off along the Thames in two groups of ten, with eight arriving in Swale and seven at Canewdon. The Acrostic in the last telegram we intercepted spelled out the message AT TARGET RDF, and I ran that past my Air Ministry contacts who at last agreed to brief me on their concerns. RDF stands for Radio Direction and Finding. I questioned this thinking it was an error and that they meant Radio Direction Finding, the navigation system we use, but apparently this is something new from the boffins on the Tizard committee. They call it Chain Home, and it refers to a new aeroplane detection system that uses reflection of radio waves to range find as well as indicate bearing from air threats. They have been experimenting with this for a while and are now building out a series of masts to give frontline warning of air attacks. The first few stations are being built in Norfolk, Lincoln and Essex to provide a ring of defence around London, and it looks like our spyclist friends are hunting for information about this technology. It is not clear if they know what it is, but it is certain that we have to stop them finding out. I am also not sure what the missing party members are doing? It can't be just more spying as their cover with the touring parties allowed them as much access as they were likely to get, so something else is up. I am hoping that the attached intercept will give us a clue. We analysed the encrypted telegram and found that it uses a classic ADFGVX cipher. It uses the same keyword for the transposition stage of the cipher as I have used for this Vigenere cipher and knowing that it should be reasonably straightforward to crack their message, but you will have to check the details for yourself as I have to go. Harry has asked me to travel to Caistor to setup a command post at the RDF tower in case we need to act quickly. If we can crack this one and work out what is going on then I hope we can mount a counter to the spyclist operation before it succeeds. Pearl.

2020/6A/solution.txt

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+Vigenere cipher
+key = RDF

2020/6B/ciphertext.txt

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+DADFD DXFGF FDFFX GADAD XFGGA DGDDG GFGGA GGAFA GGGAV GVFDD AAVAG DFFXG XGDFV GGDFD DGFAV GFADG GFFGF FVAGD FDFGA DAAFD VDVGG DDFDG FGVFA AFFXD VGGDD GFFGD GFGDF ADDVA VDVGA AVDVF GDAAA AVAFG XADAF DGDGD VAGGG DFAFF AFXGF AAFGD FGVAF FVDGF DGFGG DFGVG GFGFF FGGVF FFXDF FDFVG FGVFF DADDD GFFFV FADFA VGGDA AVDFF DFDAF DDAGG FAVGX FGGDG VDAFV DGDGG VDGGV FDDVV VADDD DDAGF GDXDA DDADD DFVDV FDFFF AGXFD GVDDG FFDDG AVGAD GFFDD AFDVD GGGFF AFVFG GDVGX DFGAF GDDFV AFFAF VDVDF GDGVF AGGGX DGDVF DGVAD GAGFG GFDFF AFDFA VDGDF DDFXF AFGDA VGDVG FGVFF FAFGF DFDGF GFDVD GAVDD GFGGG GGFGD FVAVG DDVFV DDGVF FGVDF AADFD GAFAF FAAVF VDVGG VGFFG FGFGV FVFDD DFAFV GGFFG AGFGX DFGFF XGAGF GXGGG DFFGV FDDDA FDVGG GFFDD AAVFV AXDFG VDFDD GDGDF AAAFD FAFFG GFVDV GGFVA DDFDG DVGFD GGAFV GVFFG GAAVG DGGFD GADGF DFFDF FDAFV DGDDF DAFGV GDFAG VDAAG DDFDD VFDAD DGFGD XFGDA AFGVD FFVAV AFAGG GFGDV GGGAG GFAGA AFGDG ADDDF FDAFF FGFFV AGGFD DFADG DDGVG FADAG DFFGG GFDFF FAGAD DGFGD GVFGF GDVGF FAAXF DDFGD AFGVD FGVDV AVGGA VADGA DVFVA DDGGD GGFXG VFAFD ADGXD FGFDG GGFGF FGGFF DGAAG DFVGV DVGVG VDFGV DVGVD GFAFD FGDGD ADAFF FDGVF XGGGG FFGFG VDVAD GVAFD VFGAX GAADG DDXDV GVGGG FFXGG FGAGF AFFFD FVFDF VADDG GGGGA AGVAF AVGVV VGXGG GFFVA AGFGV GGGFA DAAGV AAGDD FGADD DDDAD VDFGV FAFDA GGFFD DDDGG GVDDG DFFAV DFGVG FDFDG AFFVA DGGDF DDGXG DDFFD DAGFD VDGFV ADAGD FFVDG FFGDF GDFDV GFAAF GDFAF FFAFF DDDGF FGDVA VGDGF GDFDG VFFDD DFDFF VDVAV GGDAG GGFGF DDFDG GFADF FADAD ADFFA DDAVD VGGGA AGDGA VFDFV DDFAF VDFGD FGFVA GFXFG DGDFA DFGDV DVDGG GGFGV GGFVA DGGAD FXGGG FGVDF VVGDG FGGAG DFDAG VGDFV FDAVD AAXDA DFDGF VDGFF AFGVA VGGFV GFFXD DGAGA FVAAD AAVDF DGAFD AFFGV GFGXF XGDDG DDFDA VDVAD GVDAD DDVDD AFFFD DGVVF FXAFG AGFDF GDGVA DDVDF FGGAA DDAAD FDFGA GFGGG DFFVG DGDDD FGDFG GGFFX ADDAD FFGAF GGADF FAGDG FFDAD FGGAD FXDGD GAGFG DXADG FFVDD GVFVD GDFFF DVDVG FGVDD FFFVA GFGGG FFGAF VDVAA AFFDF FGVGX GDDAF FDFGF FGADF VAFGV AVAVF DAFFG GDGVD FGVGV GDFFD GFVDV GXGDD FDFDD FGFDG VAFFD GVFDG FDDGV GFFVA FDXGA GGDFG AAFFX GFAGD DDAAV DVAAA GFVDG DXGFD DDVDF FADVA XGFFA ADGGF VADGG GFAGG FFXDV FGGDD XGGGF FDDFF VFDGD AAFVG VDFGV AGFDG GFVVV DADAG GDFDV AAGGF XDFGV GDFGF VGDAF GGFXD ADDGV FGGAA XGVFF FFDFD ADDAA GAAFD GGFFX ADGXG GGVFD GVFGF VAVGG GXDAF DDDGG FGAVF GFFGX GGGFG GDFFA GGAFA VGAAF GVDXD GDXFD FDDGF VDFFD GFGDD GDVDF FXAFD FFVFG GXGGG GFDDF AXGGG DGVDG FXAGD FGFGF DDGVD GGGDG AXFDG DAFGF ADAXF GFGGV GADFF DDFGV GVFFA GDFDF FDAGF AAFGA AVVVA GVVGF DFAFF FGDGG FDGAF FAAGD DFDFD VFDDF FGFGD VGAGA GFFGF VGFAD AADDF DAFDD GGFAG DAFGV DDGVD FFGDG GFAGA GGDFV AFFGG FGVAA VVDAG VAFGF DGFVA AAGDD FFDGG VGVFD DFGGG XGVGV FVDGF VDGGG FADGG GFFDD AFAGG FGDDG DFGFG GDFDF AGGGF GAFGG FFGGG GFGFG DFGGD FFDAF AGDGD GGGVF VGAFF VFDDF AAGGF GDFFD DFDAD GVXGF GFVGG AGGFG DGGGG VGVDD GGFFF FDFFD FVAFF DGGFG DDDAF DGGGX DFADA XGGDA GDAGG GDFGG DFGGA VDDDA DVDFF DDGAF FFGFD GDFAD DDFGG FFXGF DFFVD GDFAF GAFFF DFDGF AVFFG GAGGF DGGVD DVVGV FXFVA FGAFX GGAFV GAGDV FVGFG DGAGV GADGF VGAFV FDFAV DFDGG FXGAA DFFFG DGGAD VAGDV FVFGF VAADG AVAFD DGVGA AGGAD GDVFG DADVF AVVAA VAGGF DGGGX DVFFG AAVDF DADDG GGFDX FDGFD VGVDD GFGDG GGFFF GGDAD VGFFX GGDDG GFGGA DXAGF DGDFV FFDVD VDFDG DADGG DGGAV DDFXD AAGGV FDGFG GFAAD DDGVD VGGGG FVAAA VAVGD GVDFF VAGDX GDFDA FDGAX DVFDF VAXVV GFADD DGVGF FFDFF DFFGG FGFAG FAGDF FFDAD AGVAG GGFGD DGVFA FGDDD AGGAG DGGXF DGFDG FVAFA DGDAG GGDDD AFVAF FDFGG GGDFG AGGFF XAAGG AFGVA FGVFA FVDVD FGGAD AGDVG GAVFG DGFFG FDGGA FXFDD XFDAA GGGFG VDDGD FGFFG FGVGA AFADV XFDDG GGFDF DFGDF DFAGG VFGDG GADDF FDGDG GFFDD FDGFF AGFFG DAVFG GFDFG FDDAD GFGVF AAVDD GVFVA GFFGV DVFVV VAVFG DFGFF XFDDD DGFVF DAVAD FAGGF XADAA DGGFG DGVDA DVDGD AGDFF GADGG XFGAD FGAGA FDDFG FGFFD FDVFV GAGDF DADGF GAGAA AGDGV FDGVG VVFFX DGDDF FFVGV DFGGG DDFDG DGDFG VFXVV DGVVG DFAFA FFFVF DAVDF FXAD

2020/6B/hint1.txt

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+5th December 2020 at 5:57 pm
+#52494
+Teymour_aldridge
+Participant
+
+I found it was really quite a step up compared to the previous problems. It required a *lot* of research, and I eventually came across an academic paper on this, which suggested using a genetic algorithm to solve it (a slightly more elegant alternative to brute force). I have an old copy of numerical recipes (it's a great book about algorithms) and after quite a lot of Rust (a nice C++ alternative which avoids lots of memory bugs which usually cause security risks) code, I was able to solve the thing.
+There's definitely simpler ways to do it (I don't recommend writing a genetic algorithm because I think it's a case of me having only a hammer and therefore treating everything like it's a nail). Note that Pearl gives some advice about what to do in 6A -- specifically around details for the transposition key. It should be easier to use an abstraction here -- consider both stages separately. To work out whether solutions are correct things like the index of coincidence are going to be your friend (because solving the transposition stage won't give you plaintext).
+I hope these aren't too many hints, but I assume (hope) Harry moderates them before these are posted to the forum so I don't give anything away that I'm not supposed to.

2020/6B/hint2.txt

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+7th December 2020 at 8:13 pm
+#52503
+Seli
+Participant
+
+For anyone who is struggling (if Harry lets this through) a nice way to do this would be to look at how you could transform it into a cipher that you can solve, perhaps even one that has come up in the competition already... From there it should all be plain sailing, Good luck!

2020/6B/plaintext.txt

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+Dear Uncle Wilhelm, The tower at Canewdon is as interesting as you had suggested it would be and I can see how it would lift the spirits of our English hosts, making them feel safe and secure in their fortress island STOP Nevertheless, nothing on the earth is forever and I think they may have a misplaced faith in this and the heavenly powers may not be strong enough to protect them from the oncoming storm STOP The local Ortsgruppe shared with me your latest gift, the beautiful clock device, and we have spent much time admiring it STOP Its simplicity is admirable and once we have learned to use it properly it will provide us all with a very high level of security STOP Safety must be our primary concern now as a lack of concentration at this point could bring disaster STOP Ralf has been given the accompanying key by the Ortsgruppe in Kent, and once we are reunited I will use this to secure our future communications STOP Establishing a safe plan for our journey home is essential in order to avoid unpleasant surprises STOP Quarrels with our host would be difficult to resolve and I would prefer it if we could slip away unremarked STOP Use of the local fishing boats might be possible, but if anything were to alarm the locals that might well prevent our departure and the clock could fall into the wrong hands STOP If you have a suggestion about how best to arrange our travel then please let us know and we will make the required arrangements STOP Ralf's party will return to London this week and will then travel to meet with us for the final stage of our adventure, when we will all regroup before returning home STOP Even if you do not wish us to proceed with our original plan then we are able to return with a whole treasure of drawings, photographs and descriptions of these important landmarks for you and your friends to study STOP Details of your wishes should be sent in the usual way using your remarkable clock device STOP Karl

2020/6B/solution.txt

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+ADFGVX cipher
+transpostion key = RDF (permutation (3,1,2))
+square keyword = ADFGVX
+
+square:
+A D F G V X
+B C E H I J
+K L M N O P
+Q R S T U W
+Y Z 0 1 2 3
+4 5 6 7 8 9
+(Z and the digits do not appear in the text, so their placement in the square is irrelevant)
+
+The first letter of each sentence of the plaintext give a secret message:
+TNT IS REQUIRED

2020/6B/tips.txt

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+Mission 6B requires you to crack a professional cipher that the German military  considered unbreakable for many years. It was  designed for use by frontline troops,  so is straightforward to implement, but very hard to crack. It is a 2-stage cipher involving  a substitution followed by a column transposition, and if you only knew that then it would be hard to crack even with a computer. Luckily the cryptanalysts at BOSS have examined this cipher for you and have worked out the  column transposition step, giving you the key in the mission briefing. If you haven’t already cracked 6A then I suggest you do that first. Since Pearl is very worried about security at this stage of the operation she has used a very tough cipher for that too, but she told you in last week’s mission briefing that she was going to do that, and what length the key will be,  so if you read that through you will see which type of cipher she has used to secure this weeks brief. Then you will have to do some research to find out how that sort of cipher works.  Agent Madness has written a supplement to our codebreaking guide to help you with this, and you can find it in the Case Files. We will ask the team if they have any more advice about cracking  the cipher in Mission 6B later in the week, so keep checking the case files section for more guidance. Harry

2020/README.md

@@ -16,7 +16,7 @@ Parts 0, 1, and 2 are practice.
     Mission Intercept 4B: Ortsgruppe
     Mission Briefing 5A: Lincoln Cathedral
     Mission Intercept 5B
-    6A
-    6B
+    Mission Briefing 6A: A breakthrough
+    Mission Intercept 6B: Pressure builds
     7A
     7B

2020/forum/52538/post.txt

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+8th December 2020 at 7:07 pm
+#52538
+Hazzataytay
+Participant
+
+This challenge is designed to test madness to their core (or anyone else), with a cipher of my own design. The only hints you will receive is that it features a unique homophonic substitution and an interesting use of the sin function. Have Fun!
+
+otxfutwebktkebddtxfbpswfmtwextxectlfamtkeaiswfbztxfysxfrtxfvskebcusweadjtxfadwtwfwsxfcptwevsxfaqtkfbjtxfawswectkertxenslfbgtxfbdytxfahslfjswfcrtxezslebgtleaitxebmtlfdvswedjtwedxtxebhskfbwtxfbcxtlfvtwfdtxfuswfbxtxebdztwfbvsxfmtkecvswfusxeajswfbcytwebrskejtxfiswfcslfbnswfbvjsxfawtkfutxfdrsweytkeaztkeacisxebntwfxtxecxtxfvtxfawswfadswfbrtledwtweczsxfxtxeakskfauswfaitxeptkfosxfvsxfbrskfbdytxfahslextwfdztwecvtweaptxfbvxtweadtxeosxfuwsxfktkfbdskeacgsxfbyskfdsxfdotwewtwfadswfbdwtwebwtwentkehtwfduswfausxebdzsxeacvsxepswfvwsxedtkebjswfbhtweauslfxsweqsxertlfboskfaddtwfbwsxedvtxfduswecuswebvtkfbdptxfaitwevsxfcgtwfdsk

2020/puzzles/8/README.md

@@ -0,0 +1,11 @@
+ANOTHER GREAT GRID PUZZLE FROM OUR GUEST PUZZLEMASTER THE LETTER WRIGGLER, whose identity, like those of all our officers and agents, is a closely guarded secret.
+
+TLW first became interested in ciphers after reading Simon Singh's The Code Book in 1998. He found the now NCC web page way back in the early 2000's and has enjoyed every years session since, but until 2019 he remained a 'lurker' never registering (because it was for schools only and did not think he should).
+
+His current interests and hobbies include electronics, recreational maths & puzzles, number theory and ciphers, and learning to play his Yamaha Tyros keyboard.
+
+![](TLW-at-Age-5-241x300.jpg)
+
+In the completed puzzle the numbers 0 through 9 appear in each of the top six rows of the grid so that they give the column sums at the bottom and no number appears in twice in adjacent cells, including diagonal adjacency.
+
+![](TLW-grid-puzzle-2-1024x718.png)