Early last year I started typing up all of Rhombus’ puzzles that appeared in Games and Puzzles magazine in the 1970s. I sent my first batch toJohn Reardon who replied almost instantly with the solutions. He also pointed out the odd typo some of which were mine but others were in the original magazine. Between us we managed to cobble together something for puzzles that were in the latter category and a zip file is available for anyone who would like a copy.

I was particularly struck by one puzzle in particular – ‘Square Hole The puzzle had his trademark lettered rectangular grid and involved three 3-digit numbers that between them contained all of the digits from 1 – 9 such that when squared their sum was a 7-digit number the middle three digits of which were a perfect square. The clues were just the grid entry letters for the three 3-digit numbers and the embedded square. The other four digits in the 7-digit number were also given.

What would have been really nice is if the three 3-digit numbers had also been perfect squares but there is only one such set which I leave to the reader to find as an exercise! [The set does sum to a 7-digit number which has a square number as its first four digits. ]

I started to look at three 3-digit triangular numbers that between them contained all of the digits from 1 – 9 and quickly discovered that there were no sets so I decided to investigate using two instead that contained six distinct non-zero digits that when squared and summed gave a 6-digit number the middle two digits of which was a triangular number. I put the numbers into a spreadsheet and did the calculations and was pleased to find that there were a number of solutions so set a puzzle and sent it to John for his thoughts. He solved it and suggested that I remove the somewhat frivolous denouement which I did.

I then turned my attention to using prime numbers instead as there are far more 3-digit primes than squares or triangular numbers. It was at this point that I wondered if I could lure some solvers into using a spreadsheet and set a puzzle that was tailor made for this purpose but with some neat clueing would prove to be unnecessary and actually take them longer! I get the impression that a number of solvers like to solve a puzzle as quickly as possible and will use any aids available in order to do this. How many solvers just read the preamble and launched straight into a spreadsheet without looking at the clues carefully?

To this end I rejected the idea of using three 3-digit primes and settled for using just two as in the triangular version. I had the spreadsheet done in a few minutes and with some conditional formatting highlighted the 6-digit results. I went through them to find those that had a 2-digit prime as the middle two digits and re-tabulated all the results. This took some time and there were just over a hundred solutions. [ I do the hard work so you don’t have to! ].

The first thing I noticed was that all the answers ended in 0, 2 or 8 which if you think about it they must do. Next was that some of the primes appeared in more than one solution set. Finally some primes remain prime when the digits are reversed or jumbled. [ Roddy would have hated this I know but if it was good enough for Rhombus then … ].

I decided that only the last digit of the 6-digit number would be given and set about constructing a suitable sized grid given that some entries would appear in more than one set and I wanted about a dozen solutions. A 7×5 looked good.

I spent a lot of time staring at my table of solutions before selecting 389 751 53 and positioned them in the grid then 157 389 59 before finally barring off the grid. The remaining solutions used would have to fit in to what was left! Setting went well and I soon had 13 clues and a filled grid.

Solvers who went down the spreadsheet route would have to find the dozen solutions I chose out of the just over a hundred that were available which is akin to finding a needle in a haystack!

The cold solve came next and I typed this up as I went along and took about 45 minutes. I read it over and realised that one clue set was redundant so removed it and checked that it didn’t affect the solution and sent it away.

AJ’s logical solution pathway is different from mine by the way and if any solver would like a copy of mine then they can get in touch.

So the precursor to this puzzle was one that was published about 40 years ago when Annie Haslam [ Renaissance ] was utilising her 5-octave range to good effect on Northern Lights [ sorry but I had to get a prog rock reference in somewhere! ] and so some solvers may ask why I do this. Is Oyler living in the past [ there’s another ]? Well yes is the simple answer! However only solvers that are well into their fifties would have experienced a Rhombus puzzle at its time of publication. Back then all that you had at best to help you was a standard scientific calculator. No computer programs or spreadsheets and solvers may care to reflect on this. This puzzle was set in that spirit from bygone days. Of course once I’ve set a puzzle I have no control as to what methods solvers use to solve it. It is after all a bit of fun and not an exam taken under exam conditions. Although that might be one way to resolve all-corrects at the end of the year and have them sit a further few puzzles – word and number – without computer/internet etc and just a copy of Chambers/ODQ/Brewer’s and a calculator. Now there’s a thought!!

The bottom line and take home message is that in any puzzle be it a crossnumber or crossword you eventually have to read the clues!

Posted on Tuesday, May 5th, 2015 at 7:36 pm under Setting the scene.
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