By Guy Jacobson

This is a twist on those old ditloid puzzles where you are given “equations” that use only the initial letters of the significant words, like “200 = D for P G in M” and you have to work out that this means “Dollars for Passing Go in Monopoly.” (This type of puzzle was originated by Will Shortz in the May-June 1981 issue of Games Magazine, where he called it Equations Analysis Test.)

The variation here is that there is a bijective cryptarithm used to map the initial letters into the digits 0-9 and vice versa.

Solvers first need to figure out the cryptarithm mapping used here, which is:

 0 1 2 3 4 5 6 7 8 9 P A F W T D S B H C

Solvers must apply this two-way mapping to the given equations to work out the full words in each one. The subscripts (which naturally become digits when you apply the mapping) specify an index into the associated word, indicating which letter from that word to use.

N: 52 = Playing6 Cards in a Deck
I: 32 = Degrees Fahrenheit9 at which Water Freezes
N: 4 = Horsemen8 of the Apocalypse
E: 37 = Plays Written by William Shakespeare5
O: 99 = Bottles2 of Beer on the Wall
N: 76 = Trombones7 that led the Big Parade
E: 1000 = Words that a Picture7 is Worth
Z: 13 = Bakers Dozen3
E: 7 = Wonders of the Ancient5 World
R: 24 = Blackbirds8 Baked in an Pie
O: 6 = Degrees of Separation9
F: 7 = Dwarfs5 in Snow White
O: 168 = Hours2 in a Week
U: 28 = Days in February5
R: 64 = Squares on a Chess Board4
N: 9 = Planets4 in the Solar System (including Pluto!)
I: 7 = Brides3 for 7 Brothers
N: 13 = Stripes on the American8 Flag
E: 100 = Cents (or Pennies2) in a Dollar
E: 7 = Days in a Week (or 8, in the Beatles2 Song)
I: 12 = Days of Christmas4
G: 180 = Degrees in a Triangle6
H: 23 = Pairs of Chromosomes2 in the Human Body
T: 101 = Dalmatians6
O: 11 = Players on a Football2 Team
N: 4 = Weddings and a Funeral3
E: 1 = Point for a Free Throw in Basketball5

The sequence of letters selected in this way, in order, spells out NINE ONE ZERO FOUR NINE EIGHT ONE. Applying the cryptarithm mapping from digits to letters to 9104981 yields CAPTCHA, which is the answer to this puzzle.

Note that a CAPTCHA is a kind of “screen test”, in that it’s a test presented on a (computer) screen, and it is intended to stop “bad actors” (in the sense of “people who do bad things”): bot programmers who try to hack in to web sites.