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COMPUTING SCIENCE

How Many Ways Can You Spell V1@gra?

Spam mutates, and the Internet community mounts an immune response

Brian Hayes

OVôI7A¨GkR0AS

So how many ways can you spell Viagra? The question is addressed directly by an amusing Web page, created by Rob Cockerham of Sacramento, whose title announces: "There are 600,426,974,379,824,381,952 ways to spell Viagra." (The page pokes fun at Viagra spam, but it carries advertisements from NetDr.com, selling you-know-what.)

Cockerham gets his number from a combinatorial analysis. He starts by tabulating the various possible substitutions for each of the five letters V, I, A, G and R. For example, any the 12 characters I, i, 1, l, |, ï, ì, :, Ì, Î, Í or Ï might serve for an I. Considering just such one-for-one substitutions, Cockerham comes up with 3×12×17×2×3×17 variations, for a total of 62,424 spellings.

Spelling "Viagra"Click to Enlarge ImageWhere do the rest of the 6×1020 possibilities come from? Cockerham observes that the spelling can also be altered by inserting extraneous characters into the word, as in V_i_a_g_r_a. Taking the basic pattern to be *V*I*A*G*R*A*, where each asterisk could be replaced by any of 192 printable characters, he multiplies 1927 by 62,424 to get the total cited above. (An addendum mentions a few more substitution possibilities, bringing the total to 1,300,925,111,156,286,160,896.)

It's always a treat to see combinatorial methods hard at work in everyday life, but I'm afraid I don't find this result quite credible. If the aim is to fool computers while producing something still recognizable by the human reader, then the pure substitutions work reasonably well. Even something as weird as V|@6®A can probably be understood if the context offers enough clues. On the other hand, applying the unconstrained insertion algorithm produces strings of characters so obscure that neither man nor machine could readily parse them. And combining substitutions with random insertions leads to nothing but cartoon cursing: g\/Sl*aT9©rÜ@´.

Ascending to a still loftier plane of absurdity, we could allow any number of insertions at any point within the word. Then Viagra would be everywhere. (In a dictionary search the shortest example I found was "vicar general.")

If we want to count only those spelling variants that are readable without cryptographic aids, we should probably limit the insertable characters to punctuation marks and spaces. At the same time, however, other techniques that Cockerham did not consider, such as doubled letters (Viiaggra), could be included. The result of this calculation would be a number much smaller than 1020, and yet even by a conservative measure it seems safe to say there are at least a million ways to spell Viagra.





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