## Listener 4216, *Evens*: A Setter’s Blog by Elap

Posted by Listen With Others on 8 Dec 2012

This puzzle was developed from November 2008 to January 2009, and was submitted in January 2010.

I like my grids to be special in some way, and I was running out of ideas. Three years ago, I was about to squirt some water at a fat-ball-stealing squirrel when the idea struck; maybe at a subliminal level the SQU got translated into SQUares, who knows. The squirrel remained dry. Within two days all seven balls, including the plastic mesh, had been stealthily appropriated.

I wrote a program to produce filled grids with rotated eight-digit squares using my trusty 20-year-old 16-bit Pascal compiler. There were rather a lot of numbers to be fitted, and so I decided to restrict them to ones which had no more than two of any particular digit, but there were still more than 16000 of them. I had the refilled squirrel water near by in case my PC overheated.

The output was written to a huge text file, and I wrote a program which analysed it, and as part of this process I recorded the distribution of the digits in each grid.

I happened to notice that there were grids with no 7s in them and decided to make this a feature in some way – after all, seven is a nice number, isn’t it? During the preparation of the rotated squares, I noticed that there was a duplicated number in the file which was formed from rotations from two different squares, and I realised that if the bottom-left to top-right line itself formed a rotated square, then the first row could contain this special case so that two lines could form the missing 7. This could form the finale. What a stroke of luck! And there were seven fat-balls… perhaps, at a deeper level, that squirrel was trying to tell me something.

I therefore reran the program with it looking for a diagonal rotated square (running in either direction) being allowed for, and one of the grids had its only two zeroes at the bottom right. Although this was unlikely to cause any confusion, I decided to use this grid.

Since the grid contained rotated squares, I decided that the clues should also incorporate this theme.

But what form would the clues take? Since the theme was squares, I decided to base the clues on a set of geometric squares, and since rotation was part of the theme, the sides of the squares could be squares or rotated squares. Since the grid had no 7s in it, it made sense to avoid 7s in the sides, perimeters and areas of the squares too. I suppose I should have avoided 7s in the clues themselves, but I didn’t think of that at the time.

Since the theme was squares, it seemed right to make the number of squares a square too!

At some stage – I think it was when the next door neighbour’s cat caught a fat, waddling squirrel on our lawn – I realised that when SEVEN was appropriately rotated it could form EVENS, and decided that all references in the clues would be even.

It took a long time to produce the clues. I decided that no clue should refer to more than three references (otherwise they might look clumsy). It was important that there was to be a clear starting point.

I wrote a program which produced all the possible even values which appeared in the grid, the first row/column being deemed to follow the last row/column as part of the continuing theme (and because I needed as many possible clues as I could get because the evenness constraint restricted the number which would otherwise be available). I then wrote a program which used these to produce all the possible clues – hundreds of them! I decided that only addition and multiplication should be used because they place much tighter constraints on possible values during the solving process.

It was then a case of looking through the possible clues to find a clue which could be used as a starting point. The next step was to find another clue which used the information gleaned to lead to another deduction. And so on. And so on. And so on. There was a new generation of squirrels in the garden by the time I had finished, but at least I knew that there was a logical path available to solve the puzzle.

My wife has not put out any fat-balls for the last three years in a futile attempt to discourage the squirrerls, but now we’ve got another pest: a BADGER. Deep holes, ruined lawn… aaaagggghhhhh!

**Elap**

## Tom Borland said

I wondered about the 00 in the bottom right and whether the ‘missing 7’ also applied here, as some sort of reference to James Bond. Was I alone in speculating along these lines?

## Simon Chillingworth said

Thanks for the puzzle it was great fun – glad that the solving didn’t take as long as the setting evidently did.

Bad luck on the badger – bet there’s more than one as well. They’ve become a increasingly common urban dweller over the last few years; Wolverhampton has a thriving population several of them feeding from the subgramineous parts of our garden.