Screen Test: Solution

By Guy Jacobson

Answer: CAPTCHA

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 = Playing_{6}Cards in a Deck

I: 32 = Degrees Fahrenheit_{9}at which Water Freezes

N: 4 = Horsemen_{8}of the Apocalypse

E: 37 = Plays Written by William Shakespeare_{5}

O: 99 = Bottles_{2}of Beer on the Wall

N: 76 = Trombones_{7}that led the Big Parade

E: 1000 = Words that a Picture_{7}is Worth

Z: 13 = Bakers Dozen_{3}

E: 7 = Wonders of the Ancient_{5}World

R: 24 = Blackbirds_{8}Baked in an Pie

O: 6 = Degrees of Separation_{9}

F: 7 = Dwarfs_{5}in Snow White

O: 168 = Hours_{2}in a Week

U: 28 = Days in February_{5}

R: 64 = Squares on a Chess Board_{4}

N: 9 = Planets_{4}in the Solar System (including Pluto!)

I: 7 = Brides_{3}for 7 Brothers

N: 13 = Stripes on the American_{8}Flag

E: 100 = Cents (or Pennies_{2}) in a Dollar

E: 7 = Days in a Week (or 8, in the Beatles_{2}Song)

I: 12 = Days of Christmas_{4}

G: 180 = Degrees in a Triangle_{6}

H: 23 = Pairs of Chromosomes_{2}in the Human Body

T: 101 = Dalmatians_{6}

O: 11 = Players on a Football_{2}Team

N: 4 = Weddings and a Funeral_{3}

E: 1 = Point for a Free Throw in Basketball_{5}

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.