Solution: Scientology

Written by Tom Weisswange

The pictures accompanying the graphs clue specific words; in order, these are:

MAYIM [Bialik]
[Groucho] MARX
[Myrna] LOY
MARY [Steenburgen]
[Bobby] FLAY

These can be grouped into pairs in which one member has an X where the other has a Y; the two graphs corresponding to this pair give the X and Y coordinates, as a function of time, of a point writing out a short piece of English text. (The reference to an Etch-a-Sketch is a clue to this, since one draws on an Etch-a-Sketch by separately adjusting the X and Y coordinates of the point that draws on the screen.) These pieces are, in alphabetical order by word-pair:

BO-X/Y: Come to
FLA-X/Y: Hunt HQ
LO-X/Y: Ask to
MAR-X/Y: use the
MA-X/Y-IM: E-meter

When solvers arrived at Hunt headquarters and asked to use the E-meter, they were seated in front of a mysterious box (the "E-meter") and handed two soda cans that were attached to it with string. They then would guess words, and were told what numerical "E-meter" readings they generated thereby; they had to figure out that the E-meter reading was "indistinct" for anything that wasn't a six-letter word starting with E, and otherwise was the number of letters their word had in common with the solution word. Playing "Jotto" in this way, they would eventually discover that the solution was ENGRAM.