The idea for this puzzle came to me whilst I was toying with setting a darts themed puzzle along the lines of Pot Black which appeared on the CC in April 2015. It struck me that 180 has a lot of factors, 18 to be precise and that the word ‘numerical’ has 9 distinct letters which is half of 18.

The most common letter/number assignment puzzles involve a 1 : 1 correspondence and in a few cases an n : 1 correspondence has been used where n is an integer greater than 1. However I couldn’t recall the case of a 1 : n correspondence and so decided to give it a go with one letter taking the values of two of the factors of 180.  If any solver knows of a puzzle that is 1 : n then I’d be obliged if they could let me know.  A puzzle is not only an exercise for the solver but for the setter also. Would it be possible to produce a puzzle with a 1 : n correspondence? Of course the next logical step is m : n where m and n are integers greater than 1.

The word has good collection of letters so the algebraic expressions in the clues could be made to form real words. The next thing to consider was the clues and how the entries would be formed. I had already used the idea of each clue giving the same answer in Problemathic which appeared in M122 – in this case 60 and the entries were just strings of digits that were formed from the letter/number assignments in the clues. I decided that each clue would give an answer of 180 but how to form the entries? I didn’t want a massive grid as before and so decided on just adding up the letter equivalents instead. This meant that the entries would be 2 or 3 digit numbers. The number of clues and size of grid then had to be considered. With 18 letter/number assignments to be found you ideally want about 18 clues but as this was a type of puzzle I hadn’t tried to set before I decided that having more clues would be preferable. A 7×5 grid looked about right so I barred it off and the puzzle would have 28 clues with 20 2-digit entries, 8 3-digit entries and 4 unches.

The letter/number assignments came next and conscious of the fact that this type of puzzle was novel and that I needed a straight forward way in I decided on the power clue M^I. Some solvers tend to give up if they haven’t got an entry in the grid or made at least some progress within half an hour so this was a way of assigning two of the equivalences quickly and giving an entry. I decided that a factor pair using the same letter would also be useful and used two with A and R. I was tempted to have each letter with one low and one high factor but thought that might be too obvious so had one with two low factors ( E ) and another with two high factors ( C ) instead.

Next were the clues and some setters who are a lot more computer savvy than I am would probably write some computer programs to do this and ease the strain. I, however, am an old fashioned, living in the past fogey and just use paper, pencil and a calculator!  So I would write down a word then underneath it their number assignments and play around with the arithmetical operators to see if I could get 180.  This took some time and many albums were given an airing during the process.  Of course it is very easy to get carried away coming up with clues like CRÈME CARAMEL etc however you have to remember that the puzzle has to be able to be solved.  Having set the way in at 14dn I needed to build on that and went for 24ac which by using just 2 letters and after a bit of calculation yielded three possible entries, two of which could be eliminated and gave up more assignments.

Many words were tried and tested and of course there were the annoying times when a good word would result in an entry starting with zero.  There were a lot of 3-digit entries to get and in retrospect I should have started off by coming up with all of them first but I didn’t and it was hard towards the end to get suitable clues. The 2-digit clues were far easier to do and I had started off with a lot of them.

The cold solve was not as bad as I’d feared and I sent the puzzle to John Reardon for his comments. His response was not only quick but favourable – the only negative being that with so few unches some entries didn’t need to be calculated which I was aware of already.

Hopefully solvers enjoyed the experience as I’ve invoked the Jethro Tull principle – again! –  and put into practice what I’d learnt from setting this type of puzzle – use a smaller grid, have fewer 3-digit entries and a higher percentage of unches.

Posted on Tuesday, January 5th, 2016 at 7:55 pm under Setting the scene.
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