Listen With Others

Under the pseudonym of Aedites, my father’s first puzzles in the Listener were mathematical until my mother suggested that he should attempt a word-based puzzle. I was the original tester for the numerical puzzles, the first of which was called “Special Agents’ Cipher” published in May 2000 and later included in the “Times Listener Crosswords” book published by Chambers in 2008. I remember this being a very nice puzzle and I was quite impressed. However, doomed as we are to compare our achievements with those of our parents, I started wondering whether, if my father was able to produce a crossword based on a code, then by rights I must surely be capable of it too.

I can only solve the mathematical puzzles, and at first, I tried considering crosswords coded numerically, but no divine inspiration seemed to be forthcoming. At some point, I started considering a letter-based 1-1 substitution cipher where all the encrypted entries were still words. However, it would clearly be necessary to encrypt common letters to common letters to get enough words in the encrypted word-list, so then rare letters would get mapped to rare letters, and we would get very few if any words in the encrypted word list including those letters. Hence it would be difficult to include them in the final grid. At some point, I realised that the way around this issue was to map rare letters to two common letters, and thus the idea of a multi-letter code for a crossword was born. It then went on the back burner for many years and if there had been no pandemic – leaving a lot of time on my hands – it would most likely never have happened.

Any cryptographic experts and other sharp-eyed solvers may have noticed that the multi-letter code is in fact a particularly bad code. For example – WHIP, WILY and WHY are all encrypted as TEERED, so someone trying to decrypt the code would not be able to uniquely decipher many words. In case anyone who knows my father (bearing in mind his previous career) would be surprised at him being associated with such a dubious code; believe me, he did remonstrate long and loud when I first suggested the idea – “You cannot possibly invent a code of which the sole purpose is for a crossword, Lysander, the Playfair code for example is a useful cipher in its own right” (well in my opinion you jolly well could). My father actually did once create a crossword where every clue answer was encrypted using a Playfair cipher; there were no unchecked letters and nearly all the clues had to be cold-solved before the Playfair cipher could be recovered, and the puzzle was deemed to be unsuitable for publication. In this case, my father thought that there would not be enough possible words, but he did advise me to have a go and see what I could manage.

I wrote a computer program to create the letter mapping for the code. This was a mixture of experimentation and optimisation to find something that worked. I was looking to maximise the number of words of length 4+, but also favouring longer words as it would be a little disappointing if all of the words in the grid were of lengths 4,5 and 6. The resulting code is probably not the best possible mapping, but I think it is quite a good one, and certainly better than most other mappings. It gave me an encrypted word list of 928 words of length 3 or more letters, including one of length 10 and seven of length 8. I then tried to use Qxw to try and create a grid, but this seemed to be hard work with the number of available words, so I wrote another program to create the grid. When the computer started coming up with acceptable grids, I sent some samples to my father. He decided that the idea was one that he could cope with after all but pointed out that I would need to include all 26 source letters in the clue answers, otherwise solvers would not be able to work out the complete code mapping. Well, it did seem to be the professional thing to do. I was spending time playing around with various grids that the computer had generated trying to ensure this, and it became clear that all the double-letter mappings need to be cross-checked in both letters in the grid so that there was no possible ambiguity in the code and all words in the grid were determined, even if Qxw gave only one valid possibility.

After spending a long time trying to force various grids to do things that they didn’t want to do, I eventually resorted to just waiting for a very long time for the computer to come up with some better grids (a very large number of grids did not have the ‘P’ of the ‘J->PR’ mapping cross-checked). Finally, the computer did come up with this grid that met the various constraints. All letters of the alphabet were used, and all but three occurred more than once. The grid contained the 10-letter word (FOLKSY->REARRESTED), and my favoured mapping for Q (QSHIP -> ALTERED). It also did not contain any words that were too close to each other e.g. FOLKS and FOLKSY. It did not contain any of the seven 8-letter words that were available, but I had already spent a very long time to get this grid, and trying to be mindful of the 80/20 rule of time management, or at least not transgressing it any further, my father and I decided that this grid was good enough. The grid had two double-unched 5-letter words, but my father thought that the crossword was sufficiently novel that it was likely to be accepted.

My father wrote all the clues, arranged for two of his friends to test it, and came up with a title for the crossword based on the encipherment of CO as STAR. He writes:

This puzzle is similar to the popular mononome-dinome cipher using letters rather than numerals. Six answers were the same length as their entry and they consist of the letters A, D, E, I, L, N, P, R, S, T and U; the other fifteen letters must each be replaced by two letters (this can be confirmed by comparing the answer length with the entry length). Hence entries can be split up into single cells and double cells, and the monographs A, D, E, I, L, N, P, R, S, T and U can be entered in their correct position. Intersecting entries will either confirm the letter if it was a monograph or else provide information about the first or second letter of a digraph. As further entries are made, more knowledge is gained about the digraphs which can be used elsewhere in the grid. Once about 2/3 of the entries have been made, it should be possible to recover most of the digraphs as a pair of monographs. The weakness of a substitution cipher is that it preserves the pattern of repeated letters in a word. The final stage is to find a simple substitution for the eleven letters that yields real words. REARRESTED is the only possibility for 9a, after which the remaining codes can be deduced.

This crossword works well as it demonstrates how a cryptanalyst must persevere on a hard problem using every scrap of information before he or she recognises some pattern in the data.

We would like to say thanks for the many kind comments that we received from people that enjoyed the crossword. This does make the quite substantial effort that we spent making it worthwhile.