Years ago someone showed me a tricky physical challenge. My (flawed)
memory of it is: two people stand back-to-back, hold hands, and then
try to untangle themselves to end up facing each other. However, that
can't be it, because I just tried it and that was much too simple.
This was a challenge that some pairs of people simply could not figure
out. I'd like to know what the real starting configuration is.

Could the challenge perhaps be that they cross their hands, or that
one person crosses their hands? I don't have someone to try these out
with, so I don't know whether they're challenging or not!

shananigans-ga

Try holding oppsosite hands, my left hand with your right hand and my
right hand with your left hand.

Greetings Bay:

Does the Human Knot game described at
http://www.jafi.org.il/education/hadracha/games/7c.html sound
familiar?

Also, see the images at
http://community.webshots.com/photo/78137448/78264304ZXhoOG and
http://www.lsa.umich.edu/mcs/yearbook%20pages/Training/

Another description of this is at
http://www.ctrforhumanisticchange.org/Newsletter/newsletter.html and
reads in part:
"Many books have been published on New Games that contain many
different types of games which can be incorporated into a lesson to
illustrate a particular concept. For example, in a conflict resolution
class to demonstrate problem solving, cooperation, and leadership, the
class can play ?Human Knots?.  The students stand in a circle and hold
onto the hand of a person across from himself or herself.  (They
should be holding hands with two different people across from them.) 
They are left with a giant human knot to untangle (without letting go
of each other?s hands)!  When processing the activity afterwards, you
can ask the students to relate the untangling to a conflict: a) some
problems are easier to solve than others; b) all parties involved need
to cooperate; c) if one possible solution doesn?t work, try something
else."

Untangling the human knot activity
http://www.unac.org/learn/wrld/lesso/session1.htm

Human Knot party game
http://www.partygamecentral.com/pgcstandard/gametmpstd.asp?gn=HUMAN+KNOT


I didn't locate an example with only two people but I hope these links
benefit your search.  Perhaps another Researcher will recall or be
able to find an example of the 2-person knot you describe.

Best regards,
journalist-ga


SEARCH STRATEGY:

untangling hands game
untangling human knot game
back-to-back human knot

There is also a famous (and fun) puzzle in topology called The
Handcuff Puzzle that is related.  See
http://www.questacon.edu.au/html/the_handcuffs_puzzle.html