Solution to Cross-stitched Words
by Herman Chau
The first step is to solve the crossword clues. While doing so, we might notice that the answers are in alphabetical order and are all six letters long. This helps us confirm most of our answers and once we have enough clues solved, we may notice that in fact the second and fifth letters of each answer are the same. Below are the answers to the crossword clues.
|Alternative to Greek salad||CAESAR|
|French pianist Alfred||CORTOT|
|They're often all scratched up?||LOTTOS|
|Title character of an Ozzy Osbourne album||MADMAN|
|Units of length in the UK||METRES|
|Star jelly genus||NOSTOC|
|Competitor to OneNote||NOTION|
|Sports with a lot of horseplay?||RODEOS|
|In short supply||SCARCE|
|Kurdistan Province's capital||SENNEH|
|Snow White's dwarves e.g.||SEPTET|
|Member of the 2021 writing team, perhaps||SETTER|
|In a way||SORTOF|
|Ring on a saddle||TERRET|
|Like the next clue, compared with this one||TERSER|
|Command to delete files||UNLINK|
The heading for the crossword clues is "Individual Cross-stitches" and at the bottom of the page is a diagram that seems to indicate a cross-stitch. Although cross-stitches are often done in rows, it is possible to make an individual cross-stitch. When an individual cross-stitch is made, it follows a cross shape as in the diagram with the thread crossing in the middle. Since the second and fifth letters are the same in each crossword answer, this suggests that we can "cross-stitch" each word such that the second and fifth letters are the crossing in the middle. For example, the crossword answer BONMOT can be cross-stitched as follows.
N T O M B
We can then attempt to fill in these cross-stitched words into the grid given. Some uncommon letters are given to us to start with. We can fill in a few words using the given letters. Note that we make an assumption in the case of the F and K that both occurrences in our crossword answers use the given letter. This is in order to try filling in the grid as compactly and efficiently as possible.
There are no further strong constraints on how to fill the remaining crossword answers into the grid, but playing around with some possible fills we find that the words intersect well, suggesting that we are doing the right thing. Some experimentation also reveals that the words must be quite tightly packed into the grid and that a greedy fill should get close to a complete solution. Indeed, just filling in the grid greedily by placing words wherever it can intersect two letters from another word gets us to a filled grid with only a couple possible ambiguities that are quick to eliminate via trial and error. The final filled grid is shown below.
Now that we've filled in all the cross-stitched words, we might notice that we haven't used the shaded red squares in the diagram at the bottom of the puzzle page. The diagram suggests that there is a recursive step where we wish to cross-stitch the filled grid somehow to extract the answer. If we look at the cross stitches present in the shaded red squares, it turns out that each of the shaded red regions corresponds to a 3×2 rectangle with some cells filled in by cross-stitches. This and the tactile nature of cross-stitching suggest that we should extract letters from the shaded red regions via Braille and cross-stitch one more time to get the final answer. Below is the filled in grid with appropriate shading to help determine the Braille letters.
Converting the Braille to letters and reading in the cross-stitch order gives the answer MANIAC.