## Czar Cycle (Solution)

#### by Yasha Berchenko-Kogan

The puzzle appears as several strings of letters in the Greek, Latin, and Cyrillic alphabets. The flavortext clues that Greek is 0, English is 1, and Russian is 2.

The flavortext clues that we should convert each letter in the message to a ternary digit depending on what alphabet it's in. We then read the ternary strings in blocks of three and convert it into a string of English letters in the usual way with 001->A through 222->Z.

To make things more fun, some letters, such as A, are in multiple alphabets and appear identically in the message. However, the constraint that we must end up with a reasonable English message should give us the cluephrase

```  SEPARATE BY ALPHABET AND SHIFT SIMULTANEOUSLY
```

Conveniently, figuring out the message also tells us what alphabet the ambiguous letters belong to. Following the instructions, we separate the message by alphabet into three messages:

```  ΛΒΞΥΒΥΒΓΚΜΒΞΒΡΚΤΒΞΒΕΜΚΒΨΣΚΤΥΚΒΞΤΛΠΓΠΡΣΒΗΕΞΚΛΒ
ANHXTXCPXIDDCDBPIXHTDGIXHVGPBBTCDHPCPUID
ЭРНЮЙЗХВХИГЗЮЭЭРЯЮЁХЧЭРЕЮЖЮЭЕЁТВСЮЁ
```

As clued, we Caesar shift the messages, keeping in mind that the Greek alphabet has 24 letters and the Russian alphabet has 33 letters. None of the shifts give phrases in their language, but one of the shifts seems more pronounceable than the others:

```  +23: ΚΑΝΤΑΤΑΒΙΛΑΝΑΠΙΣΑΝΑΔΛΙΑΧΡΙΣΤΙΑΝΣΚΟΒΟΠΡΑΖΔΝΙΚΑ
+11: LYSIEINAITOONOMATISEORTISGRAMMENOSANAFTO
+11: ЗЫШИФТАМАУНТИЗЗЫЙИРАВЗЫПИСИЗПРЭМЬИР
```

If one sounds out the first phrase, it sounds like Russian! Likewise, the second phrase is a Greek phrase spelled phonetically in English, and the third phrase is an English phrase spelled phonetically in Cyrillic. Figuring out this constraint from one of the messages should help resolve any ambiguity in Caesar shifting the others.

We then get the following transliterated messages:

```  КАНТАТА БЫЛА НАПИСАНА ДЛЯ ХРИСТИАНСКОГО ПРАЗДНИКА
ΛΥΣΗ ΕΙΝΑΙ ΤΟ ΟΝΟΜΑ ΤΗΣ ΕΟΡΤΗΣ ΓΡΑΜΜΕΝΟ ΣΑΝ ΑΥΤΟ
THE SHIFT AMOUNT IS THE YEAR OF THE PIECE'S PREMIERE
```

Translating, we find that:

```  A cantata was written for a Christian holiday.
Solution is the name of the feast written like this.
The shift amount is the year of the piece's premiere.
```

Now, what is this "shift amount"? Recalling that the first cluephrase said to "shift simultaneously," we discover that if we shifted the messages together rather than individually, we would have to shift the encrypted message by +1727 to get our cluephrases, since 1727 is 23, 11, and 11 modulo 24, 26, and 33, respectively.

The cantata which premiered in 1727 and was written for a feast is "Ich habe genug" by Bach, written for the Feast of the Purification of Mary. This holiday has a lot of other names, but only one of them is a Greek word spelled out with English letters, namely, HYPAPANTE.