I refer to the wooden snake puzzle in this post:
I notice that there are 6 solutions to the 4x4x4 snake, which start respectively as follows:
- FRB… (↗→↙…, which is also the solution under spoiler in the above post)
- FUB… (↗↑↙…)
- RFL… (→↗←…)
- RUL… (→↑←…)
- UFD… (↑↗↓…)
- URD… (↑→↓…)
Is there any logic or rationale behind the fact that the third step is always the opposite direction of the first step? Why do the other starting steps (e.g. FRU, RFU, UFR) fail to solve the puzzle eventually?