jf's Puzzles

[jnz]

For Ring Ring (hanicim) and Ring Ring Ring (kezirin): nosebab
I liked this puzzle.  I used trial-and-error instead of a theory-based approach.  Although I guess I was thinking that the machine calculates f(x) = x * (0 - x) and that would have to have a fixed-point (other than zero).  Clearly f(-1) = -1 no matter what modulus you use but I don't have any proof that some of the rest of the odd numbers wouldn't fall into a separate cycle.  Luckily things worked out pretty well.

[Rene]

For Ring Ring (hanicim) and Ring Ring Ring(kezirin): ryzoror

No modulo arithmetic here - just trying all possibilities