For beta, also the line has to turn at each dot? Otherwise the example seems not unique.

The alpha rules are nice, unfortunately some Slalom-like rules were too promising for me (no loops, then no crosses: seemed to work fine for the example and the first puzzle, but the second one is contradictory quite late).

You're right, it should also make a turn at each dot!

Example is not unique for slalom-like solution, there's one cell that may contain either slash.

Thank you for the solutions, Vladimir. I solved Gamma as "Path must alternate going through circle-wall-circle-wall..." but did not realize the additional constraint. It solved the example uniquely but obviously not uniquely for the puzzles themselves. Which might explain why I had to guess and was happy (at the time!) to reach a conclusion! :)

I thought it was a great contest. I did have one question about the incorrect products puzzle. I got an answer of 45213 and 23541 doing this the 36 was the incorrect product. Maybe I am missing something but after checking many times this seems to be a possible alternative solution.

The rules say there's just one incorrect digit. If you have a solution with 36 turning into, say, 16 or 35, please share, but I still think the solution is unique.