Hmm... Arm wrestling in 2D certainly would be an interesting affair!
Fred and his opponent (let's call him Jim) would have to either
a) Glue their hands together whilst standing up (by using jinydu's method) and then jumping over the backs of their chairs (whilst still glued together!!!), which would probably be extremely painful...
b) After managing to sit down, using an adapted version of the jinydu-glue technique to glue themselves together...
Then, they'd try and push each other away, which would cause even more problems. If Fred managed to push Jim away from him and Jim fell off his chair, then Fred would b slammed against the table edge if they were still stuck together...
1 / _
_O[__|/
|_ O/ ____ _ |
| | |\/\_ | | |
Fred is flying through the air after pushing jim away from him.
2
_ O
|_ O/ _____\\_ _ |
| | |\/\_ | /_ | |
Fred is slammed against the table aftre pushing jim away. (Yes I know, just imagine they are still stuck together).
Of course, there is no reason why the rules couldn't be adapted even to more, so that if you managed to push you opponent away from you and he glue seal was broken, then you won... Or something like that anyway!
(Oh, and please don't take the mickey out of my "diagrams". They took me ages).
P.S. I just previewed my message and the diagrams got made all wonky. You'll have to do with the written explanation for the 2nd one. Sorry!