News Article

GCHQ and the IET present a new puzzle designed for STEM students and apprentices. Can you solve it?

Last Updated: 16 Oct 2017
At GCHQ, it's no secret that we love puzzles. Our work involves solving some critical and very challenging ones.

News article - 11 Oct 2017

In collaboration with the Institute of Engineering and Technology (IET), we've decided to create a puzzle especially for the readers of the E&T Early Careers magazine. Daily clues will be released here, between 12 and 15 October, with the full puzzle solution becoming available on 16 October.


We collaborate with organisations such as the IET who are committed to the professionalism of their members. The IET considers that Apprenticeships are an important route into Engineering, and we couldn't agree more!

Amongst a variety of roles for graduates and experienced professionals, we offer two degree Apprenticeships, one of which is in Software Engineering. You can apply until the end of October to be part of our next cohort of Apprentices, which will start in September 2018. Visit our careers website to apply.

[Click here or on the image below for a printable version of the puzzle.]

Here's a bit of information about the puzzle to help you make a start:

The puzzle consists of an electrical circuit diagram surrounding a square of letters. The circuit consists of a cell (battery) and a sequence of smaller circuits connected together in series to form a loop. Each smaller circuit consists of a number of 1Ω resistors - at most six of them in each case. 

Clue 1

Try calculating the overall resistance of each smaller circuit in Ohms, expressed as fractions, going clockwise around the circuit. This sequence of fractions can be used to extract a message from the square of letters.

Clue 2

The sequence of fractions begins 4/9, 3/4, 11/13. The message is extracted from the letter square by taking each fraction as a set of row/column coordinates, so the message starts as follows:

4/9   = row 4,  column 9  = P
3/4   = row 3,  column 4  = U
11/13 = row 11, column 13 = Z

Complete this message, then look for a second message by using the same sequence of fractions in a different way.

Clue 3

The completed first message is:

PUZZLED? TRY LOOKING AT THE UNUSED LETTERS

The second message is found by taking the sequence of fractions in reverse order (i.e. going anti-clockwise from the cell), and using the coordinates the other way round, so the second message ends as follows:

11/13 = column 11, row 13 = A
3/4   = column 3, row 4   = Y
4/9   = column 4, row 9   = ?

Complete this message, then look at the letters that have not been used in either message (as suggested by the first message).

Clue 4

The completed second message is:

EVER WONDER WHAT A PUZZLER MIGHT DO ALL DAY?

Extract the remaining letters (working from left to right, top to bottom) to produce a third message, which has been encoded with a simple substitution cipher based on an alphabet derived from a keyword.


Solution

The unused letters are:

RVXYDPXORHAXEPZZOAMXWAXIGQAXGXWDLOTXDVXNIAFXNDXMDOQAXVRBTXDPNXFDLAXGNXKSIJXTGMIXSGLAALMXTDNXSDXTDNXPH

The codeword is 'Gustav Kirchoff', the German physicist whose Laws are used in the analysis of electrical circuits. This gives the following substitution cipher:

Plaintext alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher alphabet:    GUSTAVKIRCHOFBDEJLMNPQWXYZ

The decrypted message, using X to represent space, is therefore:

IFXYOUXLIKEXPUZZLESXWEXHAVEXAXWORLDXOFXTHEMXTOXSOLVEXFINDXOUTXMOREXATXGCHQXDASHXCAREERSXDOTXCOXDOTXUK
IF YOU LIKE PUZZLES WE HAVE A WORLD OF THEM TO SOLVE FIND OUT MORE AT GCHQ DASH CAREERS DOT CO DOT UK