Besides anagrams and palindromes, if there’s one thing wordplay aficionados like to mess around with, it’s the numerical value of the letters of the alphabet. Assigning numbers to letters—A = 1, B =2, C = 3, and so on, all the way through to Z = 26—opens the alphabet up to all kinds of mathematical and numerical games and trivia.

So add the value of ARM (32) to the value of BEND (25) and you get the value of ELBOW (57). Likewise, WHITE (65) plus HOUSE (68) equals GOVERNMENT (133). HAIR (8, 1, 9, 18) is a palindrome in this A to Z number system, as is INSULINS (9, 14, 19, 21, 12, 9, 14, 19). Add up the neighboring letter pairs in CAN (3 + 1, 1 + 14), and you’ll get DO (4, 15). The letters in FOURTEEN DOZEN add up to 14 dozen (168).

One more game that can be played with the numerical values of the alphabet is to search for words that total a specific value—the holy grail of which is precisely 100. Words that total 100 in this A to Z way are affectionately known as “dollar words.” They’re actually not all that rare in English, and a full list of them includes some fairly familiar words:

ANNUALLY BOUNDARY CULTURE DRIZZLE

MITTENS MOODIEST NASTILY OUTSET

PAYPHONE PORTLAND PREVENT PRIMARY

PRINTER SESSION SOURCES STRESS

STYLES SWIMMER TATTOOED THIRTY

TOILETS TURKEY UNDRESS USELESS

WHENEVER WHISKING WHISTLES WEDNESDAY

But given a set total in mind, that raises a couple of questions: What are the shortest and the longest dollar words in the dictionary?

Because 100 is a relatively large total for a short word (and because a lot of the highest value letters at the tail end of the alphabet are hard to find homes for, like V, X, and Z) shorter dollar words are fairly hard to come by. As a result, only a handful of 5-letter dollar words have ever been discovered, including:

BUZZY NUTTY PUSSY

In fact, as proof of just how many seldom-used letters lie at the end of the alphabet, if you were to change the numbers around so that A = 26, B =25, and so on through to Z = 1, the number of five-letter dollar words increases enormously:

ABBEY ACRID BACON BASAL

BEFOG BEGET CATCH CHAIN

CHALK CHINA DODGE ELIDE

FACET HENCE IMAGE LAGAN

LANCE MAGMA MEDAL NAKED

But shortest of all are two 4-letter words: acca, an Australian slang word for an academic, and caca, a childish word for poop.

Oppositely, it can be just as difficult looking for as long a dollar word as possible; the more letters a word has, the higher its total grows. But the relatively high frequency of the letters in the first few places of the alphabet means that there are quite a few lengthy dollar words, including some with as many as 12 letters:

BACKTRACKING COMMANDEERED

DEBAUCHERIES DESEGREGATED

INAPPLICABLE NON-BREAKABLE

Apparently longest of all is the 13-letter word adiabatically, a term from meteorology and thermodynamics referring to any process that occurs without a loss or gain of heat.

But why stop at adding up? Multiplying the numerical values of words leads to some considerably larger numbers—and some considerably higher targets.

Multiply the letters of the word TYPEY together, for instance, and you’ll end up with 1,000,000 (= 20 × 25 × 16 × 5 × 25). TEETHY multiplies to 2,000,000 (= 20 × 5 × 5 × 20 × 8 × 25). And PEYOTE multiplies to 3,000,000 (= 16 × 5 × 25 × 15 × 20 × 5). No word has yet been found that totals precisely 4,000,000 or 5,000,000, but some—like LURING (4,000,752) and JUICING (5,000,940)—have come tantalizingly close.