How many shades of gray are there?

To readers of a certain sort of fiction, there are fifty. But it's not so much the count or the color that matters as the semiotics: a suggestion of moral ambiguity explored in great detail. In Roy G. Biv: An Exceedingly Surprising Book About Color, design critic Jude Stewart explores the symbolism of shade and light. Steven Heller interviewed her for The Atlantic.

“I’ve always been strongly swayed by color,” she tells me. “I can recall as a kid poring over a 1980s self-help book, Color Me Beautiful, which shows you how to wear the ‘right’ colors for your skin tone. The before and after shots were incredible: drape her in the right shade of pink, and suddenly she’s dewy and glowing. Drape her in the wrong shade, though, and she turns sallow and shrunken, as if her soul had been sucked out.” Her book’s chapters loosely follow the order of the rainbow-referencing mnemonic in its title—red, orange, yellow, green, blue, indigo, violet. She also added in white, pink, and brown, colors “that don’t appear in the rainbow but allowed me to tell some great stories,” she says.

To answer the question, the book suggests a "million" shades of gray--an illustration of human nature's virtual infinitude. Heller's copy of Roget's International Thesaurus offers 17 english synonyms for "gray", exposing a cleverly Whorfian count. He reports that paint-maker Benjamin Moore offer "150-plus" shades of gray.
At Pantone's website, I found that it returns 104 official colors containing the word "gray", but many of them are obviously not particularly gray.
Frustrated, I was ultimately forced to consult the ultimate arbiter of any question regarding color: Crayola.