# Listen With Others

## Listener 4230, Elm: A Setter’s Blog by Quinapalus

Posted by Listen With Others on 16 March 2013

I wrote Elm before Small but Perfectly Formed (Listener 4176). Unfortunately (for me) Kea’s excellent Table-turning (Listener 4100), also involving a grid dissection, was published while I was in the middle of writing Elm, and I decided to postpone sending it in for vetting. Even so, it stayed in the pipeline for a while to ensure a seemly gap between the two puzzles.

The idea behind the puzzle had been the subject of many idle doodles. Sorted by longest side, the first three ‘primitive’ Pythagorean triples—ones that aren’t just multiples of other ones—are (3, 4, 5), (5, 12, 13) and (8, 15, 17). Now 52 is far too small for a Listener puzzle, and 172 is probably too big. But 132 is just in the Goldilocks zone.

Among the doodles I had a couple of dissections of the 12-by-12 square into three pieces that could be reassembled into the 13-by-13 square with the 5-by-5 in the corner. (Exercise for the reader: can it be done in two pieces?) Here they are, displayed, as seems traditional on this site, as animated GIFs.

 First Dissection Second Dissection

It’s nice to have solvers get the scissors out, but the problem is how to indicate the intricate pattern required concisely. I hit upon the vaguely apt idea of using deleted letters in entries to indicate where the scissors should go, taking advantage of the natural correspondence between the points where letters are omitted in lights and grid lines. Deleted letters give a medium for a message as well as making the clue answers longer, always a good thing.

Once the basic structure had been sorted out I got the computer to look for suitable bar patterns. Just as carpenters don’t like exposed end grain, I wanted to avoid bars on the edges of the grids or coinciding with cuts. A symmetric final grid would give solvers struggling to find the last few cuts an alternative angle of attack and anyway is more satisfying.

Trying some candidate grids with a slightly modified version of Qxw’s filler, I found that the first dissection was likely to be a much harder fill than the second, probably because there are more cut edges and hence a greater fraction of the answers have to be of the more constrained ‘skippy’ type. Nevertheless, even filling the second grid wasn’t easy: for example I couldn’t find a satisfactory fill with a message starting ‘cut along grid lines by deleted letters’ instead of ‘cut along grid lines by skipped letters’.

With the second dissection the top left of the grid is relatively unconstrained. The fill I had found placed several of the less friendly letters in the top and bottom right, and with a bit of rip-up-and-retry it was possible to mop up the rest in the top left and make the fill pangrammatic.

Permuting the skippy clues and interleaving them arbitrarily with the others to spell out the message gains some freedom in the grid fill. Not numbering the clues covers up the resulting untidiness; and writing the skippy clues so that they appear in alphabetical order compensates a bit for the extra difficulty at the cost of making life harder for the setter, which is as it should be.

It seems possible to write a clue for pretty much any word with pretty much any given letter as the correct form of a misprint (though it’s much harder if both misprint and correct form are specified). I could therefore present these in alphabetical order of answers, with the result that solvers who read the preamble carefully would be able to deduce the type of most of the clues from the outset.

The reaction of the vetters was fortunately largely positive, though the original preamble underwent drastic pruning and some clues were shortened to have a better chance of fitting on one line.

Early feedback on That Site and by e-mail indicated, as expected, that people were finding the puzzle a bit harder than average. But most seemed to think it was worth the effort, which is very gratifying. What I hadn’t expected was that many solvers completed Grid B first: since the grid wasn’t given I thought that almost all would leave it to the end.

Many thanks to the test solvers who persevered in the face of a draft that was far too difficult; to the vetters for all the improvements they made; and to all who commented on the puzzle after publication. I greatly value your feedback.

Quinapalus

1. ### Seth Mouldsaid

Absolutely brilliant!

2. ### Dale Johannesensaid

I tumbled to the general idea as soon as I added 144 and 25. This stirred a memory, and I searched through Dudeney, finding your first dissection in Amusements in Mathematics #175. Of course this did not help. Topnotch puzzle with excellent clues, and I especially liked the mix of two different cluing devices.
Answer to exercise: no. The corners of the 13×13 are 13 apart, so no two of them can share a piece in the 12×12 rearrangement.