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Hello #mathtwitter folks! I have some cool stuff to share involving combinatorics, crossword puzzles, and math in general.
Read on for more info, but you can start with this mini crossword
I made themed around a mathematician whose birthday is today. https://www.7xwords.com/daily/04/04-03.html
Read on for more info, but you can start with this mini crossword
I made themed around a mathematician whose birthday is today. https://www.7xwords.com/daily/04/04-03.html
Assume a crossword grid must have all words length 3 or greater, white space forming one connected component, rotational symmetry around the center square, and no border of black squares all the way around.
How many such possible arrangements are there in a (2n+1)x(2n+1) grid?
How many such possible arrangements are there in a (2n+1)x(2n+1) grid?
That was apparently a @FiveThirtyEight Riddler Puzzle
from @ollie a couple years ago. Well, they specifically asked about 15x15 grids, which is a standard size for puzzles you see in daily newspapers. https://fivethirtyeight.com/features/how-many-crossword-puzzles-can-you-make/
from @ollie a couple years ago. Well, they specifically asked about 15x15 grids, which is a standard size for puzzles you see in daily newspapers. https://fivethirtyeight.com/features/how-many-crossword-puzzles-can-you-make/
The thread linked below has some answers and info about that.
SPOILER alert: There are some 347 quadrillion such grids!!! https://twitter.com/Log3overLog2/status/1092472516571000839
SPOILER alert: There are some 347 quadrillion such grids!!! https://twitter.com/Log3overLog2/status/1092472516571000839
And the page linked below on the OEIS (Online Encyclopedia of Integer Sequences) has some numerical values for other odd x odd square grids.
Note the combinatorial explosion! But also note that there are only 312 grids for the 7x7 size...
http://oeis.org/A323839
Note the combinatorial explosion! But also note that there are only 312 grids for the 7x7 size...
http://oeis.org/A323839
312 = 6*52, so one could publish a new puzzle every Monday through Saturday for an entire year and see every possible 7x7 grid *exactly once*. Neat!
Here they all are in these four images:
Here they all are in these four images:
And hey, that's exactly what @malisolves is doing with her website #7xwords!
Check out the "why?" page ( https://www.7xwords.com/why.html ) for more info about the project, and check out the full page of all the grids (puzzles playable in your browser): https://www.7xwords.com/index.html
Check out the "why?" page ( https://www.7xwords.com/why.html ) for more info about the project, and check out the full page of all the grids (puzzles playable in your browser): https://www.7xwords.com/index.html
It's cool that people could sign up for specific days/grids, so lots of different constructors are contributing their styles and voices to the project.
And today, April 3, is the day I signed up for
Here's that puzzle link again so you can try it: https://www.7xwords.com/daily/04/04-03.html
And today, April 3, is the day I signed up for
Here's that puzzle link again so you can try it: https://www.7xwords.com/daily/04/04-03.html
And here's a blog post I wrote about where the idea for the puzzle came from:
https://wordsxing.blogspot.com/2021/04/7xwords-04-03-2021-and-my-math-themed.html
https://wordsxing.blogspot.com/2021/04/7xwords-04-03-2021-and-my-math-themed.html
And, hey, if you liked seeing mathematical names and terms appearing in a crossword puzzle, then check out my book! https://bit.ly/MiniMathCrosswords
I made 64 puzzles, each a 10x10 grid with two theme answers running horizontally. Sometimes they're similar terms (FRACTION / RATIONAL), sometimes they form a phrase or name (SRINIVASA / RAMANUJAN), or sometimes they just have a linguistic connection (WEAK STAR / POWER SET).
Meanwhile, the rest of the grid is full of math words/names. All but a few entries have something mathy in the answer or clue. For example, you'll see MATLAB, OPENSET, ANOVA, and NOETHER, and you'll see TIE clued as: "A math teacher might get one with formulas on it as a gift."
I realize they're challenging because of specific trivia knowledge, but I'm hoping the small size and themes will help, and I believe a lot of fun will be had in looking up answers and learning new stuff. I certainly learned a lot while researching everything and writing clues!
Here's a page on my (new as of yesterday) academic website where you can try a couple of the puzzles that are in the book and see if you like them. Two playable applets on the page http://bit.ly/MiniMathSamples
http://bit.ly/MiniMathSamples
Even if you're not a typical crossword fan, I think that you math folks reading this might enjoy my puzzles because they avoid the tricky wordplay of, say, the NYT crosswords and instead focus on featuring as many mathematical words and names as possible.
No matter what, I hope you enjoy reading about this fascinating intersection of combinatorics, crosswords, and coding, and I hope you enjoy any puzzles you try!
(I promise to only tweet about crosswords here when it overlaps with math, like this stuff
)
(I promise to only tweet about crosswords here when it overlaps with math, like this stuff
)
And feel free to DM me for more info about this stuff, especially if you're curious about how to get involved with solving/making crosswords. Happy to help or point you to resources!
