## Enigmatic Variations 1491

## Pioneer by Wickball

## Setter’s Blog

Extra letters spell RICHARD FEYNMAN’S JEWEL, a reference to the formula in the second row; changing LEOPARD and RULER produces LEONHARD EULER, PIONEER of both discoveries.

I first got the idea for this puzzle from a question on the BBC1 quiz programme ** Only Connect. **After a considerable incubation period, the baby finally emerged which I sent to the Sunday Telegraph. I was dismayed to find that, although the idea was accepted, the grid failed the EV constraints on two counts.

Firstly, the average entry length was a little too short (although not for the clue answers before compression). This was correctable by some minor tweaking.

Secondly, one entry, NOT FAR, at the bottom of the first column, was not in Chambers! Try as I might, I could not find a 6-letter alternative which would preserve theme letter F and also the A, since A SALTI would not budge without upsetting the machinery which produced the rest of this formula. Finally, I opted for the 5-letter OFFAL. This led to a fairly major reworking of the top-left quadrant and, to retain symmetry, the bottom-right. I was sorry to lose quite a few of the original clues, although I was pleased to retain the one for AIRSPACE.

Grateful thanks are due to Steve Bartlett, the EV editor, for his patience and his help in tidying up some dodgy clues.

Richard Feynman, who truly had a “brain the size of a planet” (to quote D Adams), was right to be in awe of the upper equation, although I can understand how it would mystify anyone with a non-mathematical bent. It manages to combine the 5 most fundamental quantities of Maths, most of which are seemingly unrelated, in the most elegant way.

Two of them are not whole numbers and can never be expressed exactly and one is not even a real number! Nevertheless, there they sit in an exact relationship, no fudging needed to make things fit. I think it’s an amazing result and it would not be beyond a good A-level Further Maths student to follow its derivation.

The lower equation is a lot more down-to-earth. Take something like a large potato and use a sharp knife to remove a number of flat slices in various orientations and you can produce a multi-faceted solid of your own design. If you then add the number of faces to the number of vertices (corners), the answer will always be exactly 2 more than the number of edges. Another amazing result. (Don’t forget to clean up the mess!)

Mr Euler was definitely a very bright fellow.

A full review of this puzzle can be seen over on fifteensquared.

Loved it. And what a blast seeing Euler’s identity emerge! That equation still gives me goosebumps. It’s part of the reason I pushed so hard to give my son the name Euler (unfortunately, my wife shot that idea down without hesitation).

Thanks for sharing, Wickball. I’m now interested in learning more about these editorial standards (average entry length, etc). I’m also curious about the type of non-Chambers words/phrases that actually are allowed. I’m guessing findable proper nouns and words in other mainstream dictionaries? It’s all very interesting.

Lee, it’s a vast topic. We have to stick to a mean word length of 5.5 or more, only a certain number of unchecked cells are allowed (say 2 in a 6-letter word, 3 in an 8-letter word and so on). There are lists of accepted abbreviations that differ for different outlets. Our total word-count should be 400 to 450 and only Chambers words are allowed or Collins or OED if we stretch it – and none that might offend (and some people are very easily offended!) You can use a given number of anagrams, hidden clues, homophones etc. but must spread them evenly and not use the same device word twice – and there’s a lot more. Don Manley’s Crossword Manual is a great help if you think you might compile – do have a go!

Wow! I apologize for ever taking that stuff for granted. My respect for setters (and editors) continues to grow! It also looks like I’ll be adding another book to my library.

Lee – you might find the Listener setters’ guide (available as a download on the Listener website) to be of interest. And I dare say that the editors of the other newspaper themed cryptics (EV and the Inquisitor) would send your theirs on request.

Found it. Thanks, Ifor! I derive a lot of unexplained pleasure from reading instructions, standards, and style guides. It might help me become a better solver, too.

My goodness I didn’t realise how much went on behind the scenes. A heartfelt thanks to all the compilers and editors who put so much time and effort into producing such entertaining puzzles.

Fortunately it wasn’t necessary to understand the equations to complete the grid. Once Richard Feynman’s jewel appeared a quick Wiki search told me all I needed to know. Interesting to see that the idea for the theme originated from Only Connect, my favourite quiz programme.

Thanks to Wickball and The Numpties.