As compared to the earlier Z408 and Z340 ciphers, we are not working completely in the dark when it comes to attempting to decode the Z32. We are, indeed, given specific details pertaining to both the content and the form of the hidden plaintext.

As to content, once decoded, we will have reached a short text that will give us the location of a supposed bomb which we would then be tasked with trying to pin down with the aid of the Phillips 66 map which we are also given.

“The Map coupled with this code will tell you where the bomb is set.”

This is hardly enough in itself to be of specific help, and so we are later given a further postscript that provides details as to the form of the plaintext.

“PS. The Mt. Diablo Code concerns Radians & [#]inches along the radians.”

with the ‘#’ (“number of”) having been added in as something of an important afterthought. (Note, however, that the author of this postscript does not also add ‘#’ before the first “Radians.”)

The use of the word “Radians” in this context is clearly problematic, as it leads us initially to think about the relevance of this term to angles in ‘radian measure’. This cannot, however, be claimed, with certainty, to have been the author’s intention, without then being faced with having to explain the semantic oddity of “inches along the radians.” If we are working with radian measure ‘radian’ is, in this context, a unit of angular measure, and the idea of measuring out a distance “along” an angle has no meaning.

Thankfully, at this early point in the analysis we are not required to commit ourselves to any specific interpretation of what is intended by the word ‘radians’ here, still retaining the ability to be able to investigate a little further whilst keeping our options here open.

What we must have, however, under any reading of the instructions as given, is a plaintext that starts by giving a bearing that identifies a specific radial line projected out from Mount Diablo as centre on the map, and a range, or distance therefrom, to be measured out in inches.

As to the former—the bearing, or angle—we are then to heed the numbering around the compass rose drawn for us over the origin on Mount Diablo, indicating some number ranging from 0 to 12, likely non-inclusive.

This, then, gives us quite something to this point alone.

We can propose, then, that the start of the plaintext will be one of the following words, the actual form being dependant upon how the bearing is precisely formatted:

• ONE, FIRST;
• TWO, SECOND;
• THREE, THIRD;
• FOUR[TH];
• FIVE, FIFTH;
• SIX[TH];
• SEVEN[TH];
• EIGHT[H];
• NINE, NINTH;
• TEN[TH];
• ELEVEN[TH].

Likewise, supposing that we are afforded the freedom to do so, we would first want to propose that coordinates alone complete to the end of the cipher and that the last six letters spell ‘INCHES’ preceded by a number that, perhaps, may also contain a fraction.

Only, as will be seen on closer inspection, these two propositions are, in fact, incompatible.

With the word ‘INCHES’ assumed to be at the very end of the plaintext, we already fix the key association:

Δ → ‘S’

Only, under the second paired constraint regarding the symbols of the ciphertext (2nd = 32nd), this requires that the second letter of the plaintext must also be ‘S’ and this, as we have seen, is not an option as none of the proposed starting numbers have an ‘S’ in the second position. Indeed, from the alternatives that we have proposed the triangle symbol would need to decode to one of the following:

Δ → ‘N’, ‘I’, ‘W’, ‘E’, ‘H’, ‘O’ or ‘L’.

This very finding, we can argue, ought then to be taken as a clear indication that the specification of the co-ordinates (bearing, range) as they appear in the plaintext does not, of itself, complete the whole cipher.

There is yet something else that comes after ‘INCHES’.

And, in one sense, this shouldn’t really surprise us, as it matches the straightforward way in which we communicate location information in our everyday language.

Let’s say that I’m arranging our first meeting and I send you a message telling you where I will be. I write:

4th and Hudson

as that is where you will find me. But “4th and Hudson” is a busy, wide intersection and I realise this just before sending the instruction. I then correct this oversight with the addition:

4th and Hudson. NW corner

or:

4th & Hudson. ATM

assuming there to be a bank on one of the corners.

Likewise, with coordinates such as bearing/range specifications.

Suppose we’re arranging some or other covert exchange away from prying eyes. I want you to pull up behind me off the highway and come over to my car and get in. I send you:

I80 W mile marker 242

This conveys the bearing (west along the I80) and a ‘range’ (mile marker 242). But, what if you get there and there are several cars pulled over? Which do you get in? I notice the potential for confusion in time and send you:

I80 W mile marker 242. White Acura

In each of these examples, we are starting with enough information to get you to the immediate location of the meet-up and then, in addition, an item of pertinent information that will pin things down precisely.

I want to propose that this is what we should be looking for with the Z32 also, and that the very specific choice of the constraint between the second and the final letters is included specifically to indicate precisely this.

Such considerations followed through might then suggest the following as a starting point in attempting to decode the Z32:

In any event:

1. the first word of the plaintext is going to be a spelled-out integer number (or its ordinal equivalent);
2. the very last letter of the plaintext is going to match the second letter of this number (or ordinal); and
3. this letter is not going to be ‘S’.