The cache is not at the coordinates given; these are the coordinates from a mobile phone and TV repeater mast in Emmer Green. The actual cache location is within a couple of miles of this, but the mast is not a sensible place to park or anything.
The puzzle can be completed in the field with paper, pen and phone, but if it’s a cold day, you might prefer to do it somewhere warm instead. The cache is a small magnetic bottle. You might need tweezers, you will need your own pen / pencil / stamp.
Numbers Stations are strange transmissions that you can hear on shortwave radio. They have a mysterious reputation. This is partly because shortwave can make things sound more strange and spooky, partly for the music or sound effects that are used to announce the transmission, and partly for the unreal-sounding automated voices reading out numbers. Because they are only sets of numbers, it’s not easy to tell much about what’s being transmitted, which means there are loads of conspiracy theories about them. It’s easy to imagine that in the world of people who try to find secrets of others, while obfuscating their own, creating some nonsense transmissions might be a way to tie up your opponents’ efforts – so some of the broadcasts might just be dummies!
The concept is that organisations use numbers stations to talk to their spies in foreign countries. The only equipment the spy needs is a shortwave radio receiver – not something that’s suspicious in most countries. They listen at their allotted time on the allotted frequency, and if there’s a message for them, they quickly copy down the numbers. They can’t reply using the radio – it’s just a radio receiver – but it works for sending messages over huge distances, and the spy can buy the radio locally so it looks innocent.
Unsurprisingly, not many cases of their use have come into the public domain, but there’s at least one case where the transmission was to be decoded using the spy’s previously-issued, single-use decryption key, called a one-time pad. The spy agency encrypts the message using the office copy of the pad, and the spy uses their own copy to decrypt it (and then destroys the sheet from the one-time pad). As long as the sheets are never used again, it’s unbreakable. If they are ever used again, or if they get hold of the sheet, an eavesdropper can use the patterns linking the two messages to break both.
Let’s look at a fictional message from a numbers station, and an illustration of what the decryption might look like. Here are the numbers heard from the radio:
28926975681067490682…
The receiver will break the digits into pairs:
28 92 69 75 68 10 67 49 06 82 [X]
Then they will look at the one-time pad sheet, which might look like one of these:
Example 1:
=32 87362 283 762 [A]
10 17 22 02 19 32 25 05 35 31 [E]
27 30 00 09 29 07 18 07 11 32
17 05 00 31 12 22 29 12 35 14
18 23 20 24 34 11 27 31 29 25
07 24 22 32 21 18 10 28 08 08
33 03 21 34 05 05 06 05 32 15
25 24 19 06 11 25 07 27 22 08
18 31 27 00 31 24 00 02 31 07
23 28 23 06 19 06 12 06 30 24
Example 2:
+44 07754 253 281
30 12 16 23 33 03 11 17 28 19
13 13 13 06 34 24 21 15 13 07
20 04 29 04 23 10 08 31 02 04
25 24 19 06 11 25 07 27 22 08
03 07 14 17 01 13 05 05 35 26
03 32 26 34 33 05 13 02 07 30
20 01 20 13 22 26 14 32 23 17
30 34 11 23 27 27 19 17 10 24
32 01 27 32 11 28 17 26 19 10
There will be some information [A] indicating how this sheet is to be used, followed by rows of random numbers – [E] is the first row. The receiver might add the received pairs of numbers [X] to the one-time pad numbers [E] to get a new set of numbers, [C]:
28+ 92+ 69+ 75+ 68+ 10+ 67+ 49+ 06+ 46+ [X]
10 17 22 02 19 32 25 05 35 31 [E]
--- --- --- --- --- --- --- --- --- ---
38 109 91 77 87 42 92 54 41 77 [C]
The spy needs to convert these numbers [C] back into letters and/or numbers. Perhaps they work with a 36 character alphabet, like this:
a b c d e f g h i j k l m n o p
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
q r s t u v w x y z 0 1 2 3 4 5
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
6 7 8 9 [F]
33 34 35 0
To get the numbers in [C] back to numbers in the range 0 to 35, to fit with the letters A-Z-0-9 [F], the spy might use modulus arithmetic. This is simpler than it sounds – for each number, we divide by 36 and just keep the remainder. For example, the first number in C is 38. We divide by 36, and get 1, remainder 2. So, 38 mod 36 is 2, and that’s the part we keep. The next number is 109; 109 divided by 36 is 3, remainder 1, so 109 mod 36 is 1. Here’s the whole of [C] and then each number in [C], mod 36, called [D]:
38 109 91 77 87 42 92 54 41 77 [C]
02 01 19 05 15 06 20 18 05 05 [D]
b a s e o f t r e e
Finally, we can convert the numbers into text, using table [F], which gives the impression that the spies might just be geocaching. At this point the spy should destroy the sheet from the one-time pad, and never use it again, so that eavesdroppers can’t later find it and decode the message themselves.
Links for the still interested (not required for doing the cache): https://en.wikipedia.org/wiki/Numbers_station