3. Placing the Black Squares

For this series, we are putting together an 11x11 grid where a major Canadian city - in this case IQALUIT, the capital of Nunavut - is embedded, as it would be in a wordsearch. 

Let's start with placing it down, going diagonally down the grid. Right now, it looks obvious to find, but it will be much harder for the solver once it is surrounded by blocks and other letters.

IQALUIT will be the wordsearch bounty of this crossword.

This theme doesn't impose much in terms of constraints: to go back to this section on the theory of the grid, we could explore any sort of symmetry that we wished. We'll keep this puzzle solidly in the mainstream, with diagonal symmetry.

To recap, as we build the infrastructure that will welcome the other words of the grid (everything that is not 'theme' is called 'fill'), we need to keep two rules in mind:
  • Every word is at least three letters long.
  • Every white square is connected both horizontally and vertically to other white squares.
Within those rules, what can we do to smooth our path going forward? 
Some letters are more common than others, and some letters are more common in certain places - the start of the word, the last letter, someplace in the middle. The most interesting letter we have here is by far the Q, with Scrabble players recognizing how difficult it can be to satisfyingly place a Q. We're playing with different rules than Scrabble players do, though: FAQ is very much something we could include in a crossword (but that would not be accepted in competitive Scrabble), while QUAERE would be rather less welcome in a grid.

That sort of decision - what we want to see in the puzzle, what we're not interested in - is what we've built into our wordlists. We can help keep your wordlists Canadian.

Knowing that we need to expect difficulties in that quadrant, let's break it up with some blocks. While longer words tend to be both more unique and less common in crosswords, they are more difficult to work with: for a seven-letter word, there are seven points where we need to find acceptable words that cross it; for a four-letter word, we only need to find four intersecting words.

There's a balance, though: people play your puzzle to solve a puzzle, not six tiny puzzles held together by a thread. 

A closed-off grid.

Above is a grid that would be described as very 'closed': if the solver is completely stumped on the top-left corner, they need to be able to crack 10-Down (the cells marked 1) to get in. They can have filled out the entire grid, but if that singular clue isn't calibrated right for difficulty, none of it will help them get into that corner. 

It's hard to provide a mathematical rule to define 'openness', but it's a little easier to show in examples: in the grid below, if the solver can't get any traction in the top-left, they can get in through one of the three columns marked.

A more open grid.

That's a final result, though. How did we get there?

Blocks along the side.

The first consideration is the sides of the grid. Because of that pesky three-letter minimum, our options are quite constrained:
  • We cannot have an unaccompanied black square in the second row/column, because this would give us a one-letter entry. Likewise, we cannot have an unaccompanied black square in the third row/column, because that would give us a two-letter entry.
  • However, we are very strongly incentivized to have squares in those rows and columns, because the alternative would be weaving together eleven-letter entries around the entire grid. 
    • While doable, it is difficult enough that this is a noted feat amongst constructors.
  • This means that the sides of the grid are mathematically bound to have those protruding lines of black squares, referred to as 'fingers'.

Our smaller grid size (11x11) means that we can break these outer boundaries into at most three words per row: 3 three-letter words, plus 2 black squares separating these, makes for a total of 11 squares. We've done this across the left and right sides of the grid; across the upper and lower boundaries, we've opted to put our black squares in the middle, giving us two five-letter entries on either side. This arrangement - as opposed to the converse, which I'd initially played with - starts the solver off with meatier entries, rather than a staccato of three-letter fill. 

Grid with optional 'helper squares'.

That arrangement allows us to consider adding something called 'helper squares' (or 'cheater squares'). Our decisions on where to place black squares were made with the help of constructing software, which assess in real-time whether or not it could create a viable crossword with your wordlists and the proposed arrangement of black squares. Sometimes, a grid that you hoped would work out gets a veto from the software - but that doesn't mean the end of it. Depending on your software, you can figure out the deadlocked part of the grid and manually fill it out; or you can play around with adding additional 'helper squares'.
The squares do not break up one long word into two, like our fingers across the grid; instead, they are tucked into a corner, and shorten the two words intersecting there. That's what's happening with the black squares added in the grid above: the grid is now simplified, as the words that must intersect are now shorter.
One or two of these in a grid won't hurt - people can't enjoy a crossword that wasn't made. The 'cheater square' name and reputation only really kicks in when there's an overuse of them, like in the grid above: having so many helper squares clustered so closely together creates an unappealing mass of black, and starts to distort the 11x11 grid shape that we'd chosen.
If I had been making a special shape - grid art - that argument goes out the window.

Blocks in the centre.

With the initial decisions made regarding the sides of the grid, let's start playing in the centre. This is where we need to most carefully balance our concern for interconnectivity/openness, and any risky letters. 
As previously noted, Q is the most concerning letter. However, we have the entirety of the English language at our disposal. After putting a block two squares below the Q, my constructing software flashes red, warning that there is only a single option that can fit there. However, that option is IRAQI - a perfectly valid option, and not one that seems to unduly limit my choices going forward.
Placing that square, and building a tiny staircase down-and-to-the-right, breaks up the long rows and columns; while allowing the solver to go either above or below the staircase when navigating the grid. 

With the general bones in place - and with the flexibility to add helper squares here and there - we're not set to pick our words to go.