# Listen With Others

## Listener 4177, Number Plates: A Setter’s Blog by Xanthippe

Posted by Listen With Others on 10 March 2012

The inspiration for this puzzle was due to the wonderful Derek Arthur. In 2010 he wrote that he was short of ‘entertaining numerical puzzles at the easier end of the spectrum’. I’m not sure if this was at the easier end of the spectrum, but I hope it was entertaining to most. Anyway, I decided that I’d try my hand. It was always going to be a combination of numbers and letters (probably because I tend to prefer letter puzzles).

As with all puzzles an idea is required — I settled on States early on (it’s a theme I used in my second ever puzzle — Unzipped in The Independent Saturday Magazine Puzzle in the mid 90s). I played around with conventional grids but nothing really worked, and lots of 2-digit entries is not good. After some time away from it I settled on number plates — there’s no connection but I figured that the similar sounds might help, the giveaway 50 entries was not part of the puzzle at this point as you’ll see later. I’m usually pretty good at getting the idea into a grid provided I’ve got enough flexibility, and so it proved. It was pleasing to get the 50 states into the grid with 12 plates.

Next for the clueing. This was interesting as you have to devise a way of giving enough information that the solver can get the solution (without the need for anything more than a calculator and logic — something Derek favoured and so do I) but not too much information that the answers just get written in all over the grid (I expect the ideal would be a single logical solving path). With flexibility as to how the across entries were divided, I gradually worked through looking for connections with primes as ever proving very useful (I was not pleased that there was a 4 digit prime, as this is not easily checked with a calculator — however, it was not needed to get to the solution, other than that the last digit had to be odd). Eventually I had a set of clues I believed worked.

For my letter puzzles I’ve never used a test solver (probably because when I started setting I didn’t know anybody suitable — however, my wife does get asked regularly whether a particular string of words makes sense for clue surfaces). For numericals, I realised that a test solver was crucial as if you make a mistake in the logic the whole thing falls to pieces. I asked the crossword community and received many kind offers — Mr E was first off the mark (!). After a little while he came back saying he was stuck — sure enough I’d said an entry was odd when it was even, doh! Fortunately, Mr E stuck with me and made many good suggestions, particularly with the preamble (he suggested I could make the definitions more difficult but I decided not to, as I wanted solvers who were struggling with the solution to be able to get extra help if needed from the definitions). He was positive about the puzzle and noticed that the other 12 states were coded in the puzzle in the number part of the plates. My initial intent had been not to mention this. He also commented that the best puzzles have a final twist and if I could work this in so that the solver needed to realise the missing 12 states were there, this would be good.

I looked for some time at adding an ambiguity in the number parts of the plates but realised that this would only be possible with major rework — I didn’t fancy that! However, with relatively little change I realised I could introduce the ambiguity that ended up in the final puzzle and off it went to the vetters just over a year ago.

I was delighted when the vetters came back at the end of last year to say they were going to publish it. The main changes were improvement to the notation and a change to explicitly tell solvers where the other 12 thematic entries were (my original wording was ‘Solvers must resolve an ambiguity so that the completed grid is thematically complete’). I said I preferred the original wording (mainly I think because it didn’t point solvers to 50 which leads quickly to US states). However, bearing in mind some of the feedback I’ve had regarding the ambiguity, I think the vetters’ wisdom has saved me from significant ire!

It’s interesting that many of those who were not happy about the square root ambiguity seem to be mathematicians! I decided to ask my son (who’s 13) what the square root of 25 was and he said 5; anything else I asked, to which, without much thought, he said -5. For those who didn’t like the ambiguity, I apologise, but I hope that it was worth it for those who found the ambiguity an enjoyable additional PDM.

Thank you for all the feedback. As to whether I’ll write another numerical — initially it was no, fun though it was I prefer letter puzzles. However, then I had another idea….

Xanthippe

1. ### John Stablersaid

I thought the ambiguity was whether to put ADD or AND in row 9, either of which could be defined by “join”. I put AND, giving NE for the down-entry state. To avoid duplication in column 2, cells 4 & 5 I put DE, giving ID in row 4. Isn’t this valid?
However I fell into the trap of putting 2109 in row 7, giving NM instead of NY, not spotting the duplication in row 4.

2. ### Paul Taylor (@aPaulTaylor)said

If anyone’s after further number-crossword fun, me and my co-crossworder @stecks have made a little one as part of her occasional puzzle enterprise Puzzlebomb: