### One greedy cat and a snail on drugs by Oyler

How many narrative style mathematicals have there been in The Listener Crossword since it moved to *The Times*? To save you the trouble of going to the website and trawling through the years I’ll tell you. It’s two and both were set by Polymath. *A Harrowing Time* L3477 in 1998 had 1078 correct entries and *Pyramid* L3632 in 2001 got 889 correct entries.

The crossnumber genre has a couple of techniques for clueing entries namely letter/number assignment and number definition. In order to make the latter type more interesting setters would introduce a theme and use a narrative in that this would hopefully appeal to crossword solvers as there was more reading to do and elements of humour could be brought in. The narrative also helps to eliminate various possibilities from lists of numbers or sets of solutions. The classic is *Little Pigley Farm* that first appeared in *The Strand* magazine in the 1930s and subsequently in many other publications usually without attribution or acknowledgement that it had appeared elsewhere – even *The Listener* fell for it and published it in 1949 as L988. In that puzzle solvers have to discover the closely guarded secret which was the age of the farmer’s mother-in-law! That puzzle also goes under the title of *Dog’s Mead* in some publications. Another puzzle that appeared was in *Mathematical Pie* and entitled *The Egg* and solvers had to work out the age of the egg. That puzzle used a grid that looked like a face and had bars as well as blocks. In 2001 issue 27 of *Tough Crosswords* published *Aunt Auguta’s Will* by Tangent which also appears in his book *Cryptic Cross Numbers* by John Enock. A further book *Fun With Figures* by L H Clarke contains 5 narrative style crossnumber puzzles. The narrative type of puzzle isn’t as common as you’d think although there are some examples on the internet.

After I retired in 2013 I wrote an article for the Mathematical Gazette about setting crossnumber puzzles. It was whilst writing that article that I realised I’d never set a narrative type puzzle before and set about rectifying that situation. The result was *t20* which appeared as EV1118. Of course I got totally carried away and continued with many others of this style mostly with a sporting theme. The results can be found on Derek Harrison’s Crossword Centre for a snooker themed puzzle and The Magpie for a golf one. All of the others have appeared in CQ under the pseudonym of Moog – got to get a prog rock reference in somehow! The book *Challenging Crossnumber Puzzles* by Oyler and Zag also contains *Who Stole The Ascot Gold Cup?* which was set for The Listener Dinner in Harrogate in 2015. Copies of the book are still available and details can be found at http://www.crossnumbersquarterly.com.

I must have been watching lots of repeats of Morse or Lewis with all the colleges when I had the idea of using a fictitious college as the theme for a narrative type puzzle and it was set shortly after the appearance of *t20*. As I mentioned above a number of the others of this style that I’d set involved sport and this proved to be a stumbling block for some solvers who were not au fait with cricket, golf, chess and snooker! Tangent’s puzzle also mentioned above involved a clue that was someone’s PIN so I decided to use that for the dénouement.

Strangely I started with the title by looking for the patron saint of mathematicians and found St Hubert. I went with convention and used a blocked rather than a barred grid. David Scott Marley set a puzzle for CQ entitled T*he Book Signing* which was a narrative type puzzle but he used a barred grid instead as this provided a much better fit for what he required.

In previous puzzles I gave solvers the choice of two dates as the way in and they had to find the correct one. Regardless of which date it was though solvers would always be able to put in 2 or 3 digits into the entry. This time I decided to use the date the college was founded and have it in the 17th century so that 16 could go in immediately.

Of course colleges have quadrangles and I decided to use this, having not just one but two quadrangles, one a square and the other a rectangle that was linked to the other in some way. The nice thing about Imperial units is that the conversion factors aren’t just powers of 10 and as I was at school when Imperial measurements were still used I went for lengths in feet and yards. (One of my physics teachers at school was a young chap called Mr Tomlinson and he delighted in setting problems involving obscure units, his favourite being furlongs per fortnight!)

So the quadrangles have an area and a perimeter and having a clue that asks for the perimeter of the Great Quad in feet and another which asks for the area in square yards means that the perimeter must be a multiple of 12. Using the 6 from the date as the middle digit for the perimeter clue means that only nine cases need to be calculated as the entry is a multiple of 4 it has to end 0, 4 or 8 and it has to divide by 3 so the digit sum must be a multiple of 3. So we have 360, 660, 960, 264,564,864, 168, 468 and 768. By making the area of the Great Quad a 4-digit entry rules out 360, 264 and 168. I wanted it to be 864 with 5184 as the area. One of our cats Tango, sadly no more, appeared in *t20* and I felt that the balance should be redressed and that our other cat Flo should appear. Now Tango’s prey of choice was of the feathered variety whilst Flo (Fibonacci) prefers fur and as the puzzle was set in a college it would no doubt have a cat. Having the cat catch a 2-digit Fibonacci number of mice would fit well as it would remove 960 and 768 from the list. That still left four possibilities and I realised I could give information in the preamble as well that solvers would use and by having it divisible by its number of factors forced the entries 864 and 5184 with the cat catching 55 mice.

How solvers go about solving a puzzle is entirely up to them and some may have looked at 2-digit numbers greater than 31 that were divisible by their number of factors. Those numbers are 36, 40, 56, 60, 72, 80, 84, 88 and 96 then multiplying each by 12 gives only 72 and 80 as possibilities.

Puzzles of this style have a lot of reading involved and it is easy to overlook some deductions that can be made. I decided to use two PINs in the puzzle, one for The Master and one for his wife with the second one having to be written below the grid. Having both as the product of 3 distinct 2-digit primes limits the choice somewhat and using three that were grid entries and clueing them as *factors* of the entry that was the Master’s PIN would see if solvers would twig that those three entries had to be prime numbers! With so few possibilities solvers could deduce the wife’s PIN from the preamble alone in that two of the 2-digit primes had to differ by 24. The 17/41 pair fail in that multiplying by 11 or 13 yield an impossible final digit for 16ac and the 34/47 pair is too large. In retrospect maybe I should have chosen the 17/41 pair with different clues as solvers assumed that you had to be over 18 to get married which is not the case in Scotland where it is 16.

In puzzles like these you can inject a bit of humour and so with it being set in a college I thought of various shenanigans that could occur. Having a bursar imprisoned for tax evasion, both the Master and his wife being unfaithful to one other and a snail race in Imperial units I hope did the trick. Obviously there had to be a clue linked to alcohol to appease one blogger and what better than to have it at the College anniversary dinner. Cheers!

I did a cold solve and sent it away without any test solvers being involved. If I had then they would have picked up on a few omissions in the preamble like forgetting to mention that the measurements were in yards. I now use test solvers.

My original puzzle was written in the 3rd person however the editors changed it to the 1st person presumably due to space constraints and added the Time Travel department, a name for the snail as well as giving more information for 13dn. That information was required in order to eliminate the possibility of 16ac being 43507 and testing if it was a prime in that its factorisation is 139×313 which takes a long time to get with a basic scientific calculator. Now I know that solvers will just have gone ‘ Alexa – is 43507 a prime number? ‘ or used Google but the rules are the rules and a standard scientific calculator is all you need and is all that is used for the pathway that’s published on the Listener site. If you choose to use a computer or use the internet then that’s entirely up to you. I personally use my Casio calculator that has a factorisation function and cost less than £10.

Reading the various comments that appeared on some sites it seems that the introduction of the Time Travel department muddied the waters somewhat which was not the intention. It may have been better to say that the puzzle was found in the college’s archives instead. However I only thought of that once I’d read the comments.

My thanks go to the editors for having the guts to publish this bit of whimsy and finally the star of the puzzle, the college cat examining the fan mail that was much appreciated by both of us!