Puzzle #3 – Solution

This post is written only for completeness reasons. The answer to puzzle #3 was almost immediately given in the comments. I will just repeat it here.
The important observations are that XOR (X,X) = 0 and that XOR(X,0) = X The solution is therefore:

Operation       Result
---------------------------------
X = XOR(,)     X^Y,Y
Y = XOR(,)     X^Y,X^Y^Y = X
X = XOR(,)     X^X^Y = Y,X  done!