I first became acquainted with the graphic art of Maurits Cornelis Escher in the mid-1960s, and quickly became a fan. So much so that in 1969 I wrote to him, and was delighted when he replied – his letter is a treasured possession. He died three years later, leaving behind an amazing collection of thought-provoking pictures.

This background was my motivation for trying to create a puzzle relating to one of Escher’s works. I knew of one other – in the August 2004 Magpie, Charybdis had provided a puzzle based on Escher’s Bat/Bird/Bee/Butterfly drawing of 1951. So what aspect of Escher’s work should I choose? I decided on the “impossible triangle” which inspired his 1961 lithograph “Waterfall”. This was appealing as it suggested a novel grid with triangular cells. I hadn’t seen many such grids, and was soon to discover the probable reason why they are rare! The triangle itself is often termed the “Penrose Triangle”, as it was devised and popularised by British mathematician Roger Penrose, though it turns out it was discovered earlier by “father of the impossible figure” Swedish artist Oscar Reutersvärd.

My first attempts at designing the grid assumed across entries and two sorts of “down” entry, with bars employed in the usual way. It soon became clear that the topology of a triangular-celled grid gave very little scope for this approach, as it is extremely hard to get the unching right. After trying a number of alternatives, I settled on a bar-less grid with meandering grid entries. At this stage I’d also decided how the impossible triangle in the grid would be indicated to the solver, and had produced an unambiguously-filled grid meeting the layout constraints, which also had the word WATERFALL in place.

I had no real idea if such a grid would be fair to impose on solvers, and so called on the help of my trusty test-solver to check this out before I wrote any clues! Filling was found to be possible from a (randomised) list of answers, but unreasonably taxing. At that point, I introduced gaps in some of the cell edges (one per grid entry) so that the first two letters of any answer could be entered, and I increased the number of words in the grid. Both would give solvers a better chance of making progress. It was now time to write the clues.

I find devising clues an enjoyable process, and always made more so if there is a clue gimmick involved. In this case, apart from the extra letters generating a message, I hit upon the idea of grouping the clues in threes, with no obvious start point, to reflect the nature of the triangle to be found in the grid. It was fun trying to get a single “story-line” to run through each triple. It was then back to my test-solver for further vetting and refinement of the puzzle. My thanks to him/her! The completed puzzle was then submitted to the Magpie team, where it got a good reception.

Feedback from solvers was almost universally positive, and some very encouraging remarks were made. Most solvers seemed to twig the reason for the title, it being a play on the first two of the three meanings of “force” in Chambers. A couple of people referred to plausible alternative answers, e.g. FIBULA for ROTULA (42), and CLEW for TAEL (43). This eventuality is always there, and such possibilities won’t necessarily be spotted before publication. I’m sorry for any problems this caused. At least five pairs of eyes looked over the puzzle before it was published!

Thank you to all solvers who took the time to comment, and to the Magpie editorial team for accepting and publishing this puzzle, with special thanks for beautifully rendering the grid.

There are many websites referencing Escher’s work. The official website is a good place to start, and I can recommend Escher and the Droste Effect.

Posted on Monday, March 22nd, 2010 at 8:46 am under Setting the scene.
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