I'm starting to get the hang of it through trial and error, but I have no idea how to explain it.
Here are two puzzles i've gotten, directions to solve them, and what you'll get for solving them that way. It seems the reward is either tied to what puzzle it is or how many moves it takes you to finish the puzzle.
(the one I got was Herding.. might be random, might be specific.. should be changed though, as even random that's a bit much and not a good idea to put something to inscrease skill that much in an easily farmable spot)
I solved the first 3 times that way and got a pedestal each time, so it should be the same so long as its those specific puzzles solved that way. Hopefully these two solutions will help someone figure out how it works.
*edit*
Got the second one again and finished it the same way and got 30 silver serpent venom.. I have no idea how this reward stuff for it is handled. Looks like it might be determined when the board spawns though.. just got something different for the other one as well.
*edit the 2nd*
Another solution, and two more rewards.. hope the moulding board gets switched for something else to curb whining.