I have this wooden puzzle composed of 25 y-shaped pentominoes, where the objective is to assemble them into a 5x5x5 cube. After spending quite a few hours unsuccessfully trying to solve the puzzle, I finally gave up and wrote a program to try all possible combinations using backtracking. Analyzing the results revealed that for every solution found, the computer made - on average - 50 million placements and removals of pieces. This is obviously beyond my capabilities as a human, even if I can see a few steps ahead that a partial solution leads to a "dead end".
So, my question is this: given that the puzzle is so symmetrical, is there some way to significantly prune the search tree (maybe even making it possible for me to solve the puzzle on my own)?
(sorry for the poor quality)