Listen With Others

This puzzle originated in an unusual way for me. I had heard of computers being used to solve crossnumber puzzles as opposed to the more limited role applying Excel and the like during the solving process. That got me to thinking about the kind of puzzle that could make life difficult for a computer whilst preserving the challenge for normal solvers. Amongst my candidates, manipulating answers before entry seemed a good possibility. I settled on the particular choice of removing 2-digit primes for two main reasons:

• there are 21 of them and 21 entries represents a reasonable sized grid,
• duplicate answers can lead to identical entries, complicating life for the computer.

At that stage I had no idea how I was going to implement the idea but set about constructing a suitable grid for the 21 entries. Given the answers were 2-digits longer than the entries I restricted the entries to a mix of 2- and 3-digits to reduce as far as possible the calculating workload. The 6×6 grid looked promising to work with and that is what I used.

The question then was where to go from there. The only information solvers could determine was that with 21 entries all of the 2-digit primes appeared in the answers and had to be cut. It soon became apparent that to make progress the clueing was going to have to be more elaborate than normal. I realised that labelling the 2-digit primes would provide additional flexibility by allowing cross referencing between clues and primes and also between the primes themselves.

The way in needed to be manageable which pointed to 2-digit entries and some restriction on choice of prime. I began by considering squares that included a reversible prime and this yielded 2 sets of pairs of squares each including a prime and its reverse. That quite nicely gave me 4 entries which just had to be positioned. Helpfully one entry was the reverse of another. Using that information, I only needed to find a way of fixing one of the entries to establish the position of all four. After some experimenting, I chose the locations 5ac,17ac, 3dn,15dn for the square clues with their positions fixed by the 15ac clue. That in turn gave information about the 6dn clue and things proceeded from there. I tried to introduce some variety into the successive steps whilst preserving the level of difficulty despite the reducing number of available prime deductions. It would be an understatement to say that this was an intensive calculation process with the constraint of allowing for ambiguous answers to precise entries but in the end it all came together.

I hope no computer solver was too thwarted in solving the puzzle. With hindsight I think trying to set a puzzle in this way with this theme contributed to a more contrived end result. Compared with my usual puzzles I felt it was not as playful as I would like, was heavy on calculation as opposed to logic and the clueing was somewhat inelegant. Nevertheless it seems to have provided a satisfactory challenge. Congratulations to all who tackled it and thanks to those of you who have provided feedback.

Zag