In the months that saw the release of the albums Animals by Pink Floyd, Songs From The Wood by Jethro Tull and Works Vol I by Emerson Lake and Palmer, Games and Puzzles magazine published a series of three articles written by Rhombus on the setting of crossnumber puzzles.

As a teenager I had collected about 50 issues of the magazine. Unfortunately when I moved home from Saltcoats to St Andrews I found that they had gone missing. Some years ago John Gowland, a setter living in South Africa, contacted me about crossnumber puzzles and in particular those by Rhombus. It transpired that his puzzles were very much in the Rhombus mould and dealt mainly with poker hands! In our communications he mentioned puzzles that Rhombus had set and that had been published in Games and Puzzles magazine along with a series of articles on how to set them. I have to confess that I didn’t remember any crossnumbers appearing in G&P let alone articles on how to set them. So as a Christmas present to myself in 2012 I purchased a complete set of the magazines on ebay – how sad is that?

In these articles he described the setting of a puzzle that involved the cubes of the first nine positive integers. The grid was one of his customary rectangles, 7×4, and the clues were the sum of two distinct cubes that gave a three digit result and of course didn’t contain zero. Of the 36 possible bicubes only 23 fitted the bill – 126, 133, 152, 189, 217, 224, 243, 341, 344, 351, 468, 513, 539, 559, 576, 637, 728, 737, 756, 793, 854, 855 and 945. Fifteen of these had to be fitted into the grid which is shown below.

Prospective setters or those interested may care to undertake this exercise!
After having read the articles my first thought was to have the clues as the sum of 3 distinct cubes that gave a three digit result but with zeros allowed. There are 84 possible tricubes and of these 64 fit the bill. You will have noticed that the grid Rhombus used is asymmetrical and has just under 40% unches. I looked at rectangular grids but couldn’t find anything suitable so opted for a 7×7 square with the central cell missing instead. I prefer to have my puzzles with a much lower percentage of unches, in this case 25%. Scanning through the 64 possible entries revealed that two were themselves perfect cubes – 216 and 729. I decided that both of these would appear in the grid in that if needed that information could be given in the form of an equation in the clues if the puzzle proved to be too hard. I toyed with the idea of having the central cell blank and have solvers having to place arrows (↔, ↓ etc ) in appropriate positions in that cell to indicate a thematic entry – namely a cube. Of course that would depend on whether or not I could fit them in!!

I started by placing 729 and 216 in the middle row and then tackled the bottom left hand corner. That done I edged upwards to the top left and outwards to the bottom right. I was left with the top right hand quadrant and no matter what I did I couldn’t get a fit. The 216 was the problem. I moved it but still no luck. I was at the point of starting all over again when I noticed that with a small change in the bottom left 216 could appear and the rest fell into place.

Clue writing was simple to say the least. Then to the cold solve. I stared at the clues for ages and realised that I had broken the cardinal rule – I hadn’t set a way in. I’d been so preoccupied with the grid filling aspect and overjoyed at having fitted the numbers in that I’d forgotten about the most important thing of all. Pride as they say …. . I would have to resort to my skill as a solver, now sadly on the wane, to find a way in which is never a good idea.

I resorted to a constructing a frequency table of the number of occurrences of each letter which revealed that K appeared least often and so solvers would suspect that it would be 729 but it didn’t prove it. Ah! Then inspiration struck. Take them two at a time. This revealed that certain pairs never occurred in the clues, CK, KT and KU. The letter K was common to all three non-pairs so had to be 729. The numbers 343 and 512 were from a choice of the 3 letters C, T and U. The TU pairing could be eliminated fairly easily by considering the bottom right hand corner but the other two required a list of all possible entries and some sustained logical reasoning before the correct pairing was found. After that the letter/number assignments fell out fairly quickly as did the grid fill which was somewhat disappointing. Of course with only nine letter/number assignments to find it was never going to be that taxing. Nevertheless the puzzle gave Magpie solvers another glimpse into the past and the opportunity to experience the type of puzzle that was popular in the era in which prog rock ruled the world!

For those wondering as to the year it was 1977 and the months of Jan, Feb and Mar respectively and before you ask – “yes I do own copies of them!!”

Just in case Magpie solvers don’t use Derek Harrison’s Crossword Centre Message Board I have typed up all of the 36 Rhombus puzzles that appeared in G&P and are available for those who want to indulge in some pre-internet and pre-PC ( in both senses! ) entertainment. Yes those puzzles were solved without spreadsheets and fancy programming and should be attempted in that spirit. A good number are fairly trivial if you use a computer but if you do you are missing out. Finally I have to thank John Reardon who has not only solved all 36 of the puzzles but for pointing out various typos and anomalies and for producing the solution grids that come with the package.

Posted on Saturday, March 1st, 2014 at 2:20 pm under Setting the scene.
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