The Times They-Are-A-Changin? – A setter’s perspective
The first version of this puzzle was quite different from the one that was published. A few years ago I think I read an article in which multiplications were performed from left to right and the wrong answer ensued! The title of the Dylan track The Times They-Are-A Changin’ was too good an opportunity to miss and so about a year ago I tried to relocate the article amongst my many books and journals and failed dismally! This resulted in my making up my own version in which the multiplication was done from left to right with the tens digit being put down and the units digit as the carry. In order to illustrate this I intended to use an idea from one of Piccadilly’s puzzles “A Long Division” that appeared in Tough Crosswords 11 in which solvers had to find, as the title suggested, a fully laid out division. [ Piccadilly always had all the best ideas! ].
I entered the multiplication of two 2 digit prime numbers first to illustrate the method and used definition type clues – square, 3across + 6 down, multiple of 5 down etc. There was a second grid in which the letters of the word TIMES had been replaced by a given set of prime numbers and solvers had to work out the relevant products and fill in the second grid. Using this method multiplication was not commutative so A x B ≠ B x A. It was, of course, rejected by Mark and Simon, and rightly so.
The title, however, was still too good an opportunity to let go and I came across a problem in Mathematical Pie 169 by HKM in which solvers were asked to find instances when ab x cd = ba x dc. I found 14 possible cases ( interested readers may care to find them all too! ) and so decided to use this as a basis for a reworked puzzle.
I thought about using two grids again but then realised that I could make use of the perimeter which would show that solvers had found out what was going on. The clues would remain as definition type and so I began to find a suitable grid which didn’t take too long with a paper and pencil. I barred off the perimeter squares that contained the x and = first and then others in a symmetrical arrangement that would force solvers to show that they had conquered the theme. At this point the rest of the grid was not barred. I put in the perimeter multiplications and then placed the two examples. An easy way in was needed and I spotted two 27s so one could be a cube and the other with a digit added above a prime so that was barred off symmetrically. In the previous version I had used clues involving consecutive ascending and descending digits and I wanted to use them again so went a bit overboard and used 4 of them barring off as I went along. The digit sum and digit product of entries was another type of clue I didn’t use very often so decided to rectify that! Then there were the annoying linked factor/multiple clues to put in. The rest of the grid was soon filled and all that remained was to solve it cold finding a pathway through the puzzle.
I was surprised that only 40 out of 48 entries got it correct and that it was rated D. About the same time Dedication appeared which used the same style of clueing and I was disappointed that there weren’t more entries. Perhaps solvers don’t like number definition type puzzles in that they are less prone to computer cracking!