WORD SUMS are a useful tool for teaching mathematical problem solving and I like to use ONE + ONE = TWO and TWO + TWO = FOUR. It never ceases to amaze me that pupils will sit back quite happily having obtained 1 solution to the former totally oblivious to the fact that there are 15 others!

I started by looking at mathematicians EULER ( obviously ), GAUSS, FERMAT, PASCAL etc and wrote a program to find the solutions. I then mixed in maths setters. It is quite fortunate that the majority of maths setters have short pseudonyms and some even have the decency to have repeated letters! I decided to set the mathematicians aside and concentrate on the setters so that if the puzzle was well received then they could form WORD SUMS II!!

The grid was going to be the problem though. In Proton’s puzzles the grids were rectangular and asymmetric. Here however there was a very limited set of WORDS being used and the fact that there were multiple solutions afforded the option of a fig jig amorphous style grid. Solvers would have to work out which of their solutions to use in order to fill the grid. Obviously a unique way in was required and this was provided by 7 x PIE = ELAP. I started with that and gradually built outwards using the two digit entries afforded by MR and AD.

Apparently PIEMAN has not set a mathematical puzzle. I thought he had as in an early issue of The Magpie there was a puzzle using the digits 1 to 4. If I’d bothered to check I’d have found that was by Mr Magoo. The few solutions to MR + MAGOO + PIEMAN = MAGPIE meant that it couldn’t really be overlooked and anyway they were the founders of the magazine. Simon’s also pretty good at Sudoku!!

Apologies to those setters not included especially BRIMSTONE but if you will choose a pseudonym with 9 different letters it makes things kind of difficult!

The following table lists all the solutions

2 x KLAN  2 x 1784  2 x 1786  2 x 1794  2 x 1796
    ELAP      3786      3784      3796      3794
    LEON      7354      7356      7384      7386

    BART      1396      1407      1809
     x 5       x 5       x 5       x 5
    TREV      6980      7035      9045

     PIE       402
     x 7       x 7
    ELAP      2814

    TREV      9513      9613
     x 9       x 9       x 9
   ARDEN     85617     86517

   ARDEN     93675     95482
   OYLER     28473     37685
  GOOGLY    122148    133167

   OYLER     59861
  GOOGLY    355389
  PROTON    415250

      MR        41        45
   MAGOO     40922     40922
  PIEMAN    368405    368401
  MAGPIE    409368    409368

   PICC     3866     3866     6833     6833     6877     6877
     AD       47       97       74       94       32       92
   ILLY     8992     8442     8995     8775     8995     8335
  OYLER    12905    12405    15902    15702    15904    15304

The rectilinear pattern is undoubtedly ‘crossword-friendly’, so from this seed of inspiration came the task of finding a composition that worked, without being too obvious. The internet helped, but it was ultimately “Sister Wendy’s History of Painting” that offered up the Diamond painting that was to become the subject of the puzzle. The positioning of MONDRIAN himself in the puzzle was almost pre-determined by the red block, and the resultant combination of letters in black looked very promising, particularly as they still permitted such as E,S and T to be used elsewhere.

While I might have set out with the original intention of providing symmetry, this soon became beyond me, as the average light length fell and the unch count rose to intolerable levels. Ultimately, this puzzle is under- rather than over-unched and is almost certainly the easier for that. What I gave away in symmetry though, I was determined to replace with a pangram that ensured that the only letters that were not accounted for in the message, were those in ultimately blank squares.

From there the setting proved constrained (by the colour code), but achievable, and the clueing based on inter-twining messages from the ends of redundant words offered a small amount of potential diversion. Although about a fortnight in the construction, I eventually had everything nicely printed up ready to go…. and while my fingers hovered over send, I forced myself one last check…. only to discover that my scan of Sister Wendy’s version of the Diamond (which I used as the template for the working copy of this puzzle) had distorted the colours in the bottom from black to blue. Aarggh! What followed was a necessary re-write of several lights. ESSAY became E+TSAR, ELIA became ELEA, NESTLED to NETTLED, and TUNA for TINY - panic over, oxygen mask away, job done.

Solver’s comments are always greatly appreciated, and they were very positive towards this puzzle. The suggestions of grading erred more towards a B than an A, but was generally accepted as reasonable. For those who found DIRE+SIS too strained, apologies (on behalf of the Chambers phonetics department at least!), and to the solver who looks forward to seeing my attempt at a Jackson Pollock work…. well, I fear they may be in for a long wait. Thanks to all.

Here is an enlargement, which shows the shy bird more clearly.

Do you have any similar photographs of this elusive bird? If so, please get in touch.

[Thanks to Chris Boyd for the camera-work]

Feel free to come up with your own caption for the photo.

As you are probably aware, the Magpie brand has recently transitioned into the current digital format, which I consider to be throughly fit for purpose, and I am pleased with the level of buy-in to the new deliverable from our core subscriber base.
Looking to proactively take our offering to the next level, I’ve come up with some broad-brush ideas for improving the magazine’s position in the marketplace. Based on the knowledge base built from similar ventures, it’s clear that there’s only one way to move to the next level, which is to parallelise.
My plan is therefore to look to supplement the existing product with daily Sudoku.

Magpie Sudoku One (in pdf format)

Smuggling in an apology below the fold: the web site was unavailable between about 9pm (UK time) on Friday night and about 10.30am on Saturday morning. This was due to unexplained computer irrationality, which we hope won’t happen again. Chris apologises for the inconvenience.

As a way of answering some of the questions that are often asked (and some that we thought ought to be asked), we’ve added considerably to the “Help” page, which can be accessed via a link in the top menu if you are logged in.

Hopefully if you have questions they will mostly be answered there. Otherwise, feel free to e-mail us.

The idea of using Life as the theme for a crossword had been in the back of my mind for some time. I realised that the topic was something of a niche one, and that many solvers would need to do a little research to tie it down. My thoughts therefore turned to The Magpie, which has a reputation for publishing puzzles over a very wide thematic spectrum, often with the need for some research.

From the start, I wanted the solver to end up “playing” Life using the cells of the puzzle’s grid, with the end result being a pattern of unchanging cells – a “still life”. This would provide a clear end point to the solving process. There are many stable elements available, including blocks, beehives, ships, ponds, etc. that could be used. The idea of gliders “moving” across the grid was very appealing, and I set about testing how things could be arranged.

Years ago, I’d made a fairly exhaustive study of glider collisions with various objects and knew of many that resulted in a stable pattern. (Did someone say “Get a Life”?) After considering various combinations, I decided to use two gliders on a “Collision Course” that would result in an unchanging pattern of two four-cell blocks. This was pleasingly symmetrical, and the eight cells could accommodate the letters J H CONWAY. Gliders are formed from five cells, and I soon hit upon the idea of identifying them in the grid via the ten letters of GAME OF LIFE, via letter clashes in those cells.

I played around with grid sizes, and positions of gliders and blocks, until I had a promising layout. I was then ready to use Ross Beresford’s “Sympathy” software, which is a powerful tool when constructing grids with letter, and other, constraints. After trying various bar patterns, I finally found a fillable grid.

I thought it would be a nice idea to make use of various Life words in the clues, if that were possible. Over the years, a huge lexicon has built up, and I thought this might be easy to do, though perhaps it would be best to avoid such terms as hivenudger, metacatacryst, pipsquirter, sesquihat, toad-sucker, and wickstretcher! However, though I got off to a good start with “oscillator” in 1 across, I found that the idea was getting in the way of writing decent clues, so regretfully I abandoned it.

With the clues completed, it was time for a trial run of the draft puzzle. This was expertly carried out by my regular test-solver, who has my heartfelt thanks – he knows who he is! With some resulting adjustments to preamble and clues, the puzzle was then ready to send off to The Magpie. I was delighted that the puzzle went down well with Mark, Simon and Shane, and that they would make it “The Magpie Puzzle” when it was published. The new set-up at Magpie headquarters gives an admirably smooth process for setters, even down to providing page-proofs for checking. During this process, I realised that there was a serendipitous match between the 19 generations in the puzzle’s Life game, and the answer ITERATE being clue 19. So the preamble was adjusted to take account of this piece of luck.
For those who noticed, I apologise for the typos in 34 down. These are entirely down to me, and occurred early on when transcribing from my handwritten clues.

There’s a great website for playing with Conway’s Game of Life at: http://www.ibiblio.org/lifepatterns/ Click on the “Enjoy Life” button, expand the window to full screen, click on “Open”, choose one of the built-in starting patterns ……. and be prepared to be mesmerised. There are various options to play with, the most interesting (to me) being the one which gives you control over the rules of the game. I found this applet very handy when checking Collision Course.

Feedback from solvers has been extremely interesting - thank you to all who commented. I am delighted that the puzzle was so well received. The Game of Life was variously played out, with pencil and paper, chessboards, spreadsheets, newly-written programs, online applets, Mathematica … even lentils! And I’m pleased that the puzzle served to introduce a number of solvers to Conway’s fascinating discovery.