Solution to the Turing competition

Last month I mentioned a codebreaking puzzle tied in with the release of the new film about Alan Turing. The competition has just closed, but you might still be able to find it online if you feel like having a go.

If you want to know how to solve the puzzle, read on…

Note: There are spoilers below (obviously), so if you want to do this puzzle by yourself, then this is your last chance to look away.

Background

The puzzle consists of three ciphertexts and a map, which is divided into a grid of squares numbered A1, B1, C1 and so on up to L8. When decrypted, the ciphertexts identify a grid square on the map in which we are told Alan has hidden some silver.

Part 1: Monoalphabetic substitution cipher

FY VKQC KJ SNM JTWTD MJGOFT FTENGJM TS HDMSENDMY LTQC GR LQKOQMRRGJO
VMDD HUS G TF EKJEMQJMI THKUS SNM VTQ KWMQTDD GA NGSDMQ IKMR GJWTIM
SNMJ G TF EMQSTGJ RSMQDGJO VGDD EKDDTLRM G NTWM EKJWMQSMI FY RTWGJOR
GJSK RGDWMQ HTQR TJI HUQGMI SNMF JMTQHY CJKVGJO FY IQMTIAUD FMFKQY G
VGDD AKQOMS VNMQM UJDMRR G DMTWM FYRMDA QMFGJIMQR NMQM GR SNM AGQRS
KA SNQMM EDUMR SK GSR DKETSGKJ SNM RGDWMQ GR HUQGMI RKFMVNMQM SK SNM
VMRS KA RSTLDM NTDD

This was quite trivial to solve. The original word spacing has been preserved, and since SNM crops up seven times, we can immediately guess that this corresponds to the word the. If we go on to replace Tt HDetEhDeY with at bletchley in the first line, we get some easy words further down: thQee clUeR ↠ three clues, and burGeI sKFeVhere ↠ buried somewhere. The whole of the first line can then be decrypted: my worC oJ the JaWal eJiOma machiJe at bletchley LarC is LroOressiJO well ↠ my work on the naval enigma at bletchley park is progressing well. Finally, the substitution A ↠ f reveals the plaintext:

my work on the naval enigma machine at bletchley park is progressing
well but i am concerned about the war overall if hitler does invade
then i am certain sterling will collapse i have converted my savings
into silver bars and buried them nearby knowing my dreadful memory i
will forget where unless i leave myself reminders here is the first
of three clues to its location the silver is buried somewhere to the
west of staple hall

Tip: If you’re really lazy, just copy and paste the ciphertext into this automatic decryption tool.

Part 2: Monoalphabetic substitution with homophones

≈ ⟨ ⊨ · + ⊻ ⊨ ⋀ ⊻ ⟨ ⋀ ≡ ↔ ∀ ⊃ ⊕ ÷ × ∠ + ∼ + + ⊻
× ⊃ ⋈ + × ≡ ⊢ + × ∠ · ⋁ × ∞ ≡ ≈ ⟨ ∠ × ÷ ⊢ ∠ ∀ ⊃
+ ⇒ √ → ÷ ¬ ∀ ⇒ ⊨ \ × ∞ ⇔ ∼ + ⇔ ∀ ⊃ ⋁ · ÷ ⋈ ∀ ⇒
⊨ ⇒ ↔ ⋈ ⊻ ÷ × \ ≡ ∀ ⋀ ↔ ¬ ⋈ ∀ × ∞ ⊨ ⊻ ⋁ ⊃ ⊻ × ¬
+ ⊥ ≈ × ÷ → ⊤ × ÷ ⇔ ∀ ⊃ ∠ ⋀ ÷ ⊃ ⊤ ⊤ × ÷ ⇔ ∼ ⊤ ×
+ ⊨ ⟨ ∼ ⊕ × ∞ ⊨ ⊻ ≡ ⇒ ⊨ ⊨ ∀ ⇒ ÷ ≡ ∀ · ↔ ∀ ∞ ↔ 8
∼ ⋈ · ⋁ × ∞ ↔ ≡ × ⋁ ÷ ⊃ · ⊢ ⇔ ∀ ⊃ + ⋀ √ ⋀ ⊨ ⊃ +
¬ ⊥ ≈ ⋀ ⋈ ∼ ⊕ ⇔ ÷ · + ⋈ ¬ ≡ ⊥ ⊨ × ÷ ∼ ⋀ ⋈ ⊃ ⊕ ×
+ ⊻ ⊕ ⊨ ∞ ⇒ ⇔ × ⊤ ¬ + ⊻ ≡ ∀ ⊃ ⋈ ¬ ⊨ √ ⇒ ÷ ⊤ × ⊨
⊨ × ∠ ⋈ ∼ ↔ ∼ ⋈ ∀ ¬ ⊻ ⊻ ⊃ + → · ⋈ ⇔ × ⊤ ⋈ ⇔ ⋀ +
⊨ ⊃ ⟨ ÷ × ⋀ ⊻ \ ⋀ ÷ ≡ × ⊤ ≈ ⟨ ÷ ⊃ ⊥ ∞ ⊨ ⋀ ÷ ⊕ ⟨
⊕ ⊨ ⊃ ÷ × ∞ ↔ ⇒ ⇔ × ∠ × ÷ ⊢ + × ↔ ⇒ ≡ × ⋈ → ⊨ ⊤
⊤ ∼ + · ⊨ ⊕ × ⊻ → ⊃ + ⊕ ÷ ⟨ \ ⇔ ⇒ ⊻ ⋁ ⟨ ⋀ ⊢ ÷ ∼
⊃ ⊥ ⋈ ≈ · ÷ ¬ + ⊃ ≈ 3 ≈ · ⊕ ∀ ∼ + → ∞ ⋈ ∼ + ⊥ ≈
⟨ ¬ + ¬ ⇔ ¬ ⋀ ⊨ ⋈

This one was much tricker, partly because it uses strange mathematical symbols, but mostly because there are more than 26 of them. This suggests that common letters like e may have been encrypted using more than one symbol. (Or perhaps some of them represent numerals?) Let’s start by converting these symbols into something a bit more manageable (≈ ↠ A, ⟨ ↠ B, ⊨ ↠ C, and so on, with @#$% standing in for characters 27–30):

ABCDEFCGFBGHIJKLMNOEPEEFNKQENHRENODSNTHABONMROJKEUVWMXJUCYNTZPEZJKSD
MQJUCUIQFMNYHJGIXQJNTCFSKFNXE@ANMW#NMZJKOGMK##NMZP#NECBPLNTCFHUCCJUM
HJDIJTI$PQDSNTIHNSMKDRZJKEGVGCKEX@AGQPLZMDEQXH@CNMPGQKLNEFLCTUZN#XEF
HJKQXCVUM#NCCNOQPIPQJXFFKEWDQZN#QZGECKBMNGFYGMHN#ABMK@TCGMLBLCKMNTIU
ZNONMRENIUHNQWC##PEDCLNFWKELMBYZUFSBGRMPK@QADMXEKA%ADLJPEWTQPE@ABXEX
ZXGCQ

The map contains several place names that might appear in the ciphertext. But where? We know that the first two words aren’t Bletchley Park because that would require the letter B in the ciphertext to correspond to the first L of Bletchley and the P of Park. (If that’s the case, then this isn’t a monoalphabetic cipher at all and we’re barking up completely the wrong tree.)

It would be a bit tedious to examine all the possibilities with pencil and paper. If you’re familiar with regular expressions then a tool like grep will make life a lot easier. You’ll need to do a bit more work to ensure that each dot corresponds to a unique letter, but it doesn’t take long. This is what I ended up with:

Place name	Matching regex	Possible matches
BLETCHLEYPARK	.(.)(.)...\1\2.....	(none)
BLETCHLEYVILLAGE	.(.)(.)...\1\2...\1\1..\2	(none)
BRICKWORKS	.(.)..(.)..\1\2.	NMZJKOGMK#
BUCKINGHAMROAD	........(.)...\1.	(none)
CHURCHGREENROAD	(.)(.).(.)\1\2.\3(.)\4.\3...	(none)
CROWNINN	....(.).\1\1	LMNOEPEE
DENBIGHHALL	......(.)\1.(.)\2	(none)
FARBLETCHLEY	....(.)(.)...\1\2.	ADLJPEWTQPE@
GRANDUNIONCANAL	..(.)(.)..\2..\2.\1\2\1.	(none)
HOWEPARK	........	FBGHIJKL, CUIQFMNY, PQDSNTIH, NSMKDRZJ, X@AGQPLZ, MDEQXH@C, EFLCTUZN, #XEFHJKQ, CKBMNGFY, K@TCGMLB, LCKMNTIU, IUHNQWC#, #PEDCLNF, WKELMBYZ, UFSBGRMP, K@QADMXE
SIDINGS	(.)(.).\2..\1	EGVGCKE, MLBLCKM
STANLEYROAD	..(.)......\1.	@CNMPGQKLNE, N#XEFHJKQXC, QZGECKBMNGF, GRMPK@QADMX
STAPLEHALL	..(.).(.)..\1\2\2	(none)
STMARYSCHURCH	(.)...(.).\1(.)(.).\2\3\4	(none)
WATEREATONROAD	.(.)(.)(.)(.)\3\1\2(.).\4\5\1.	(none)
WATLINGSTREET	..(.).....\1.(.)\2\1	(none)

The first of these matches is unlikely to be correct because if NMZJKOGMK# decodes to brickworks, then the word that follows it must start with sbri. So let’s try the next one. If LMNOEPEE decodes to crowninn, then we end up with the following:

ABCDnFCGFBGHIJKcrowninnFoKQnoHRnowDSoTHABworRwJKnUVWrXJUCYoTZinZJKSD
rQJUCUIQFroYHJGIXQJoTCFSKFoXn@AorW#orZJKwGrK##orZi#onCBicoTCFHUCCJUr
HJDIJTI$iQDSoTIHoSrKDRZJKnGVGCKnX@AGQicZrDnQXH@CoriGQKconFcCTUZo#XnF
HJKQXCVUr#oCCowQiIiQJXFFKnWDQZo#QZGnCKBroGFYGrHo#ABrK@TCGrcBcCKroTIU
ZoworRnoIUHoQWC##inDCcoFWKncrBYZUFSBGRriK@QADrXnKA%ADcJinWTQin@ABXnX
ZXGCQ

This looks a bit more promising. In particular, it seems likely that the characters IJK before crowninn correspond to the word the, since this also gives us other sensible patterns like the word when later on in the first line:

ABCDnFCGFBGHthecrowninnFoeQnoHRnowDSoTHABworRwhenUVWrXhUCYoTZinZheSD
rQhUCUtQFroYHhGtXQhoTCFSeFoXn@AorW#orZhewGre##orZi#onCBicoTCFHUCChUr
HhDthTt$iQDSoTtHoSreDRZhenGVGCenX@AGQicZrDnQXH@CoriGQeconFcCTUZo#XnF
HheQXCVUr#oCCowQitiQhXFFenWDQZo#QZGnCeBroGFYGrHo#ABre@TCGrcBcCeroTtU
ZoworRnotUHoQWC##inDCcoFWencrBYZUFSBGRrie@QADrXneA%ADchinWTQin@ABXnX
ZXGCQ

Since T is one of the most common letters in English, it wouldn’t be surprising to find another symbol used to represent this letter. The sequence Zhe crops up three times, so perhaps Z also decodes to t. If so, encrBYt in the penultimate line must surely be encrypt.

AyCDnFCGFyGHthecrowninnFoeQnoHRnowDSoTHAyworRwhenUVWrXhUCpoTtintheSD
rQhUCUtQFropHhGtXQhoTCFSeFoXn@AorW#orthewGre##orti#onCyicoTCFHUCChUr
HhDthTt$iQDSoTtHoSreDRthenGVGCenX@AGQictrDnQXH@CoriGQeconFcCTUto#XnF
HheQXCVUr#oCCowQitiQhXFFenWDQto#QtGnCeyroGFpGrHo#Ayre@TCGrcycCeroTtU
toworRnotUHoQWC##inDCcoFWencryptUFSyGRrie@QADrXneA%ADchinWTQin@AyXnX
tXGCQ

It looks like we’re on the right track now. Let’s replace #orthewGre##ort with forthewareffort, and QtanCeyroaF with stanleyroad (another place name that was matched in the table shown above).

AylDndladyaHthecrowninndoesnoHRnowDSoTHAyworRwhenUVWrXhUlpoTtintheSD
rshUlUtsdropHhatXshoTldSedoXn@AorWforthewareffortifonlyicoTldHUllhUr
HhDthTt$isDSoTtHoSreDRthenaValenX@AasictrDnsXH@loriasecondclTUtofXnd
HhesXlVUrfollowsitishXddenWDstofstanleyroadparHofAyre@TlarcycleroTtU
toworRnotUHosWlffinDlcodWencryptUdSyaRrie@sADrXneA%ADchinWTsin@AyXnX
tXals

Now it’s getting much easier. secondclTUtofXndHhesXlVUrfollows is obviously secondcluetofindthesilverfollows. Also, AylDndlady ↠ mylandlady, doesnotRnowaSoutmyworR ↠ doesnotknowaboutmywork, W ↠ e, and @ ↠ g…

mylandladyatthecrowninndoesnotknowaboutmyworkwheneverihelpoutintheba
rsheletsdropthatishouldbedoingmoreforthewareffortifonlyicouldtellher
thathut$isabouttobreakthenavalenigmasictransitgloriasecondcluetofind
thesilverfollowsitishiddeneastofstanleyroadpartofmyregularcycleroute
toworknotetoselffinalcodeencryptedbyakriegsmarinem%machineusingmyini
tials

There are only two symbols left now — $ and %. We know Turing worked in Hut 8 at Bletchley, so $ ↠ 8. But what about %? This is easily solved by looking at these characters in the original ciphertext where the numerals 8 and 3 are used in these positions. Apparently these characters weren’t encrypted at all. Here’s the key I ended up with:

Symbol	Corresponds to	Symbol	Corresponds to
·, ⋀	A	⋁	B
⊕	C	⊻	D
→, ⇒, ⊃	E	⊤	F
⊥	G	∀	H
¬, ∼	I	⊢	K
⊨	L	≈	M
+	N	×	O
\	P	÷	R
⋈	S	↔, ⇔, ≡	T
∞	U	√	V
∠	W	⟨	Y

Part 3: Enigma cipher

Walzenlage:     III  I  II
Umkehrwalze:    B
Ringstellung:   S  B  E
Steckerbrett:   LD  ER  FA  S...?
Grundstellung:  ?  ?  ?

RPVZL YNCQO RVUSY UZUBC KNIBK DWZRP FZVLA

Based on the decryption of Part 2, it appears that these are the settings to be entered into a Kriegsmarine M3 Enigma machine in order to decrypt the final message. A quick search led me to an online M3 Enigma simulator that does the job. As per the instructions in Part 2, we should use Alan Turing’s initials for the initial indicator setting (Grundstellung): A M T. The only thing we are missing here is the remainder of the plugboard settings (Steckerbrett), which have been partially obliterated. If we use only the first three plugboard settings, this is what we get:

THENI LHERI NNODT HEANT FHOMM YLODG ISGNX

It doesn’t take much effort to figure out that S and N should be swapped around, so let’s add SN to the plugboard and try again:

THESI LVERI SSOUT HEAST FROMM YLODG INGSX

If you connect the lines running west from Staple Hall and southeast from the Crown Inn, you’ll end up at cell C3.