There is no widely recognized specific ASL sign for puzzle.
There are (of course) ways to express the various concepts related
to the word "puzzle." See below.
PUZZLED:
If you mean "puzzled" as in, "She was puzzled by his behavior" --
you should do the "question mark in the mind sign" which is done by
holding and index-finger handshape pointing up (palm side forward)
about 3 inches in front of your forehead and then quickly changing
the handshape into an "x"-handshape as you move the hand back toward
your forehead.
PUZZLE (in general)
It is very common just to spell "PUZZLE" but the spelling is
modified by using a "double Z" which is done by forming a "bent V"
handshape and tracing a "Z" shape in the air. (If you were to do
that on a dusty chalkboard or the dirty windshield of a car it would
create two "Z's"). This spelled version could be used to refer
to board puzzles or "tough to figure out situations."
PUZZLE (board game)
This sign, "puzzle" shows two interlocking pieces and should be used to mean
a puzzle that you put together.
Notes:
The two interlocking bent-V hands version of the sign "puzzle" is very close to a
couple of other signs such as
"physics" and a version of "problem." But those three signs are different.
See: PHYSICS
See:
PROBLEM
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