Asked and Answered: 12

Last year, I told you about Spelling Bee, a word game that appears daily in the New York Times.  The point of the game is to form as many words as possible, using any of the seven letters provided, any number of times, as long as the center letter is used at least once.  It is a fairly undemanding diversion which, along with my cup of coffee, helps get me going in the morning.  Plus, it gives me something to kvetch about to my friend Eric, who also plays.

Eric and I often compare notes and complaints about the Bee of the Day.  My usual beef is about the exotic foodstuffs (e.g., BOBA, CALLALOO, GHEE) included in the answer list, and Eric (former chemistry professor) and I both gripe about the chemical words, such as NICOTINIC and PROPANOL, that of course should be accepted by the Bee but are not.

Nonetheless, we were pleasantly surprised by a recent Bee in which BORON (Element 5) and CARBON (Element 6) were among the answers.  This got me wondering: what is the greatest number of element names one can generate from a set of seven different letters?

My first step toward an answer was to create a spreadsheet to count the number of times each letter of the alphabet appears in the list of element names.  Note: I decided to limit the number of elements in my list to the first 100, i.e., from HYDROGEN to FERMIUM.  Elements 101 and beyond — all man-made — are unfamiliar even to Eric and me.  One of those is darmstadtium (Element 110) of which only a few atoms have ever been produced. So it’s not like I’m disrespecting Nature by excluding darmstadtium and its ilk.

Anyway, back to my spreadsheet.  I found that the consonants appearing most often in my 100-element list were M (50), N (36), R (33), L (22) and T (22).  And as you might guess, the most common vowels were I (56) and U (50).  After spending about 15 minutes playing around with frequently-appearing letters, I was able to find two different seven-letter sets which “contain” the names of four elements.  (Before I reveal, would you like to try?)

The first set I found was EIO/BMNR. (I’ll refer to these sets by their vowels/consonants). This set spells the elements BORON, BROMINE, IRON and NEON.  And my second set was AEIO/DNR, which spells IODINE, IRON, NEON and RADON.  Interesting, but…

I was, of course, not satisfied.  Humankind needed to know: are there other seven-letter sets that spell out four element names?  And more importantly, are there seven-letter sets that spell out five (or more) element names?  I did not yet have these important answers.

So, for humankind’s sake, I was obliged to resort to brute-force computation, employing the only modern programming language I know — PHP.  I am familiar with PHP because it is the language used by WordPress, the platform for this and millions of other blogs.  And though I have a PHP reference manual, most times when I want to write code for a new task, I just do an internet search — 99 percent of the time someone has already done the thing that I want to do and has provided functions and/or code for it.

And that is (mostly) how I wrote a PHP program to print out all the seven-letter sets that spell out four or more element names.  I’ll spare you the details, but suffice it to say that before now I had no idea there were PHP functions like count_chars (finds the number of unique letters in a word), array_intersect (lists the items that two sets have in common) and implode (combines a set of individual letters into a single word).  Those functions served me well here, but they (like many other PHP functions) are so special-purpose that I can’t imagine any programmer having good command of them all.

In any case, I ultimately wrote a program that evaluated all 213,333 of the seven-letter sets containing one or more vowels and one or more consonants found in the element list. Without further delay, here are the results.

SEVEN-LETTER SETS WHICH CONTAIN FOUR ELEMENT NAMES:

SEVEN-LETTER SETS WHICH CONTAIN FIVE ELEMENT NAMES:

None.  Zero.  Not-a-single-one-ium.

So there you have it.  There are 15 different seven-letter sets which can be arranged to spell four element names, but there are no seven-letter sets that will spell five element names, at least not with respect to the first one hundred elements.

If some nerd ever uses this edition of Asked and Answered to win a bar bet, I will expect due credit, if not a beer.