Can you imagine solving the New York Times crossword puzzle without any clues? Maybe not with all of the creativity and new words and phrases appearing in modern crosswords, but with a fixed word list there's some hope. In this challenge, you create a crossword puzzle grid in which this is theoretically possible.
The challenge
Maximize the number of white squares in a white- and black-shaded 15x15 crossword puzzle grid, such that the white squares can be uniquely filled with letters so that every across and down word appears in the international Scrabble word list.
Grid construction clarifications
In US newspapers, crossword grids are usually constructed so that every letter is "checked", meaning it is part of both an "across" word and a "down" word. In the UK and elsewhere (especially in cryptic crosswords), this is not necessarily the case: if an "across" or "down" word would only be one letter, it need not be an actual word (like "A" or "I"). For this challenge, follow the more relaxed rules: single-letter words need not appear in the word list.
There are various other traditions (in the US and elsewhere), none of which need to be followed in this challenge. For example, words can be only two letters long, words are allowed to repeat, and the grid need not have (rotational) symmetry.
Is this even possible?
Yes! One can write a short script to verify that the unique solution to the following blank grid on the left is the filled grid on the right:
One can display the filled grid in a computer-readable format as follows:
###CH##########
###YE##########
###AM##########
CYANOCOBALAMINE
HEMOCHROMATOSES
###CH##########
###OR##########
###BO##########
###AM##########
###LA##########
###AT##########
###MO##########
###IS##########
###NE##########
###ES##########
Your solution
The grid above has 56 white squares out of the 225 squares total in the 15x15 grid. This serves as a baseline for this challenge. Grids with fewer white squares may also be interesting for reasons other than their score, for example if they satisfy some of the aesthetic traditions mentioned above.
Please submit your solution in the same format as the computer-readable baseline above. Please include code that verifies that there is a unique solution to your grid.
Interesting code snippets (eg for searching the space of possibilities) and discussion of how you found your grid are appreciated.
The word list
The international Scrabble word list was previously known as SOWPODS and is now called Collins Scrabble Words (CSW). It is used in most countries (except notably the US). We prefer to use this list because it includes British spellings and generally has significantly many words than the American word list. There are multiple editions of this list which differ slightly. You can find different versions of this list linked from Wikipedia, on Github, in Peter Norvig's Natural Language Corpus and elsewhere, often still called "SOWPODS".
This challenge is highly sensitive to the broad nature of the choice of word list, but less so to smaller details. For example, the baseline example above works with any edition of CSW, but CH is not a word in the American Scrabble word list. In the event of a discrepancy, we prefer to use CSW19, the most recent edition of CSW. (If we use this list, which was released this year, we can expect answers to this challenge to remain valid longer). You may query this list interactively on the official Scrabble word finder site or download it (as well as the previous edition, CSW15) from the Board & Card Games Stack Exchange or Reddit's r/scrabble.
Tldr: the authoritative word list for this challenge is available as a plain text file (279,496 words, one per line) over on the Board & Card Games Stack Exchange.
Further discussion
One issue raised in an early answer and comment is why existing crosswords (eg, in the NYT) don't answer this question. Specifically, the record for fewest number of black squares (and thus largest number of white squares) for a published NYT crossword is already the most famous record in crosswords. Why can't we use the record grid? There are a few issues:
Many of the answers in NYT crosswords do not appear on our word list. For example, the record grid includes
PEPCID(a brand name),APASSAGETOINDIA(a four-word proper name for a film and novel, written without spaces), andSTE(an abbreviation for "Sainte"). It appears that the record grid is not solvable with Scrabble words.Merely expanding the word list to include more words does not necessarily help with this challenge: even if all of the words in the record grid appeared on our word list, the solution would not be unique without the clues. It is often possible to alter some letters at the ends of answers while keeping everything a word. (For example, the bottom-right-most letter can be changed from a
Dto anR.) Indeed, this is part of the (human) construction process when writing a crossword, trying to obtain "better" words.The reason ordinary crosswords (usually) have a unique solution is that the clues help narrow down the correct answers. If you simply try to fill the grid with words without using clues, it's likely that there will either be no possibilities or many possibilities. Here's an example of three different fills (using the word list for this challenge!) for the same grid (one that's relatively frequently used in the NYT):
- Another issue raised in the comments is some amount of disbelief that this question is a coding challenge. Perhaps it is not immediately clear, but it is hard to even find a single valid answer to this challenge. Finding the baseline above involved multiple, specially-crafted search programs that were not guaranteed to find an answer. I do not personally even know of a general way to solve an arbitrary grid, if you want the answer in reasonable time. Existing crossword construction programs can help, but I assume (perhaps incorrectly) that they do not actually do a full search of the possibilities. (I used such a program for the three side-by-side grids above; this worked because that particular grid allows for many solutions.)
Grids with fewer white squares may also be interesting for reasons other than their score, for example if they satisfy some of the aesthetic traditions mentioned above.") - similarly to avoiding bonuses in code golf, I'd rather a code challenge be about just one thing. This means all the answers can be compared like for like. It also makes it clearly objective, which will help with reopen votes. \$\endgroup\$