Salomon Numbers

Here's a brag for you: I've made a crossword with a guy who made a crossword with John Lithgow. I've also made a crossword with a guy who made a crossword with a guy who made a crossword with the late host of House Hunters. (R.I.P. Suzanne Whang, gone but not forgotten.)

Hungarian mathematician Paul Erdos*(1913-1996) wrote so many papers with so many collaborators (over 500!) that by the '70s a game had emerged, where mathematicians would see how few links any given academic needed to have co-authored a paper with someone who co-authored a paper with someone who co-authored a paper (etc., etc.) with Paul Erdos. This game was codified in the form of the Erdos number: Erdos himself was a 0, everyone who co-authored a paper with him is a 1, and all those people's (non-Erdos) co-authors are a 2.

The idea took off and is now in use across a wide variety of fields. Actors, of course, have the Bacon number, after the classic Six Degrees of Kevin Bacon party game. Musicians have Sabbath numbers (as in, "have you been in a band with someone who's been in a band with someone from Black Sabbath"). Chess players have Morphy numbers, bridge players have Vanderbilt numbers, and go players have Shusaku numbers. And crossword constructors? Well, we have Salomon numbers.

Nancy Salomon

The late Nancy Salomon (1946-2021) was among the most beloved and prolific crossword constructors of the Shortz era, publishing 186 puzzles in the New York Times alone, over 100 of those grids being collaborative efforts.* Nancy was perhaps more generous with her time in assisting new constructors than anyone before or since, mentoring hundreds of would-be constructors in the finer points of crossword creation over the years and writing tons of useful primers on the art of making puzzles. I can't think of anyone more deserving of being placed at the center of this collaboration network than her.

So What's Your Salomon Number?

Thanks to the inimitable Alex Boisvert, we now have an easy-peasy way to determine your Salomon number: the Wisdom of Salomon applet on Crossword Nexus will let you plug in the names of any two constructors who've been published in a mainstream-ish outlet in the past 25 years or so, and figure out whether they can be connected. The data set isn't perfect (it doesn't have any metadata from the blogosphere, for instance) but it's definitely the most efficient tool to figure out where you stand, especially if your Salomon number trends on the higher end.

Of course, some of us don't need an applet to assist us in this matter: remember how I said that I made a puzzle with a guy who made a puzzle with John Lithgow? That guy is the absurdly prolific Brendan Emmett Quigley, whose other collaborators include Nancy Salomon (in The New York Sun, 12/20/06). So Brendan's Salomon number is 1, and as someone who's published a puzzle with Brendan (in AVCX, 5/26/21), my Salomon number is 2. (As is John Lithgow's, for that matter.) This is, of course, the lowest a new constructor's Salomon number can go, barring shenanigans.

If you'd like to tie with me and the star of 3rd Rock from the Sun, well, you'll need to collaborate with one of the 40+ people who've collaborated with Nancy Salomon over the years. Her xwordinfo page lists 30 of those collaborators, some of whom are still active constructors to this day. Salomon has also made puzzles in other outlets with such notables as the aforementioned BEQ, Vic Fleming, and Ed Sessa.

But if you're content with a respectable Salomon number of 3, though, all you need to do is find someone with a Salomon number of 2 and ask them to make a grid with you. (Hint hint.)

Mass Collaboration

Of course, we're currently assuming that a crossword can only be co-authored by two people. That's not necessarily the case - consider this puzzle I did on Ross Trudeau's blog with both Ross and Sally Hoelscher, which simultaneously counts as a collaboration between me and Ross, Ross and Sally, and Sally and me. Four-way collaborations exist too: via Rossword Puzzles we get this beaut of a grid made by Amanda Rafkin, Robyn Weintraub, Wyna Liu, and Aimee Lucido.

But you know what? That's amateur hour. Here's a byline for you, from the AVCX in 2013:

Well, Deb Amlen and Brendan Quigley both have Salomon numbers of 1, which means that Francis Heaney, Tyler Hinman, Matt Jones, Aimee Lucido, Caleb Madison, Ben Tausig, Byron Walden, and Zoe Wheeler all have Salomon numbers of 2. Bam!

But we can go a step further here, thanks to Erik Agard. In 2014 he wrote a puzzle with clues by... deep breath... Evan Birnholz, Peter Broda, C.C. Burnikel, Gladys Cassidy, Jim Cassidy, John Cassidy, Mike Cassidy, Regina Cassidy, Tom Cassidy, Mario Choi, Marie Desjardins, Caroline Diehl, Anne Erdmann, Sam Ezersky, Neville Fogarty, Tyler Fultz, Jeff Gellner, Gabe Gonzalez, Brian Goodall, Angela Olson Halsted, Amy Hamilton, Peter Hammond, Erin Iverson, Chris King, Bob Klahn, Adesina O. Koiki, Andy Kravis, Amanda Lee, Phoebe Mcbee, Erin Milligan-Milburn, Charles Montpetit, Linda Murray, Cy Neita, Peter Ostrander, Amy Paepke, Owen Paepke, Amy Reynaldo, Bruce Ryan, James Schafer, Thiagu Sezhian, Nancy Shack, Michael Sharp, Loren Muse Smith, David Stein, Vega Subramaniam, Guy Tabachnick, Tom Tabanao, Lena Webb, Zoe Wheeler, Stella Zawistowski, and Raina Zheng.


Since Bob Klahn has a Salomon number of 1 thanks to a collaboration in the NYT from 1998, this means that this puzzle singlehandedly gave 50 people (including Agard himself) Salomon numbers of 2. Wow!

Erdos-Bacon-Salomon Numbers

The existence of both Erdos numbers and Bacon numbers has led some to the invention of Erdos-Bacon numbers, which are just the sum of a person's Erdos and Bacon numbers. You can concatenate even further, if you're so inclined: a popular blog attempted to determine the Erdos-Bacon-Sabbath numbers of various celebrities, for instance.

So is there anyone with a finite Erdos-Bacon-Salomon number? Yes, actually. As part of the New York Times' "celebrity crosswords" series in 2017, Andrea Carla Michaels (Salomon number 2) made a puzzle with Neil deGrasse Tyson, making NdGT's Salomon number 3. Tyson's Erdos number is 4 (via an article in COSMOS) and his Bacon number is 2 (via a cameo in Zoolander 2), so his Erdos-Bacon-Salomon number is 9.

Can we go lower than that? I asked around, and got an e-mail from my AVCX colleague Byron Walden, who claims his Erdos-Bacon number is 6. This is pretty easy to back up: he co-authored a paper about... Euler's totient function? sure... with Peter Hilton, whose Erdos number is 2; Walden appears in the documentary Wordplay alongside several bona fide celebrities, including Jon Stewart, whose Bacon number is 2. And as we've established earlier, Byron shared a byline with Brendan Quigley, who shared a byline with Nancy Salomon. So 3 + 3 + 2 = 8. And that, I think, is the lowest an Erdos-Bacon-Salomon number can feasibly go.

...unless, of course, Kevin Bacon wants to try his hand at crossword construction.

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