# Listen With Others

## Listener 4101, Primordial: A Setter’s Blog by Viking

Posted by Listen With Others on 18 September 2010

Mathematical puzzles appear four times per year and the series editors like to offer a variety of style and difficulty in any one year, to help retain the attention of solvers who do not attempt word-based puzzles. It turned out that the puzzles currently available failed to achieve either objective and so I reluctantly decided to try to construct one myself.

I started with the idea of prime numbers since they are fascinating for many. I soon thought that a grid consisting only of primes might work. There would need to be a reasonable number of two-digit ones, and it might be ill-advised to exceed three digits. I constructed a grid and filled it. Then I noticed that few of the cells contained even digits, so I wondered if I could banish them altogether. I made the number of two-digit cells equal the number of such primes and started to play around with the three-digit slots, with particular attention to the centre, aiming for palindromes to help fix the two-digit entries. It was only much later that I realised I could perhaps use all three-digit primes of this form. This was duly achieved.

I now considered how to clue the puzzle. The traditional way would be to use cross-references, eg, 28ac = 5 x 23dn + 2, but this looked unpromising because of the very nature of prime numbers: there could be no factors to use. Also, I reminded myself that the puzzle was meant to be of a different style. I was starting to realise that the nature of thr grid fill had opened up the whole puzzle to attack by treating it as a jigsaw of primes. This was unfortunate but I reasoned that the intention was to have a puzzle that was on the easy side and that it was up to solvers to decide for themselves whether they wished to flex their arithmetic muscles. So, I set about providing clues that would allow a reasonably easy computational solution. I was gratified to hear that some solvers deliberately chose that route. Another factor influencing this was that the puzzle would appear at Bank Holiday time and some solvers might be abroad with no access to lists of primes or even a calculator.

Test-solving of the first version proved that it could be completed by arithmetic (and some easily constructed sub-lists) but that some of the test-divisions needed a calculator. The final two lists were added to temper such divisions and I believe nothing worse than division by 11 is needed until very near the end.

See http://www.listenercrossword.com/Solutions/S2010/Notes_4101.html for a full explanation.

Viking (Derek Arthur)

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