This is the so-called "QuaternaryBox". It takes 1536 moves to open. About ten years has passed since thecreation of "Ternary Box". It was designed for the International PuzzleMeeting of 2010.
“Binary Box” has a “U”-shaped groove for the trick. The “Ternary Box” has an “S”-shaped groove. Therefore, since the creation of “Ternary Box”, thedesigner thought that the "Quaternary Box" could have an “M”-shaped groove somehow. But, in fact, the "Quaternary Box" also needed a groove that isshaped like a “Comb”, not only an “M”-shaped groove. “U”-shaped groove, “S”-shaped groove and “M”-shaped groove have no branches. So, I will callthe grooves like them as “Snake”-shaped grooves. On the other hand, I callthe groove that is just like “Comb”, “Comb”-shaped groove. Thus, it isexpected that an “Even Number Notation Box” is made of “Snake”-shapedgrooves and “Comb”-shaped grooves, and an “Odd Number Notation Box” is made of only “Snake”-shaped grooves.