Q. Is this true that Rav Miller forbids playing with a Rubik’s Cube on Shabbos due to borer? Is this a chumra, or me’ikar hadin it is assur?
An additional shailah. Since the cube can be taken apart without much difficulty, by rotating the top layer by 45° and then pulling one of its edge cubes away from the other two layers. Consequently, it is a simple process to “solve” a Rubik Cube by taking it apart and reassembling it in a solved state, is this permitted on Shabbos?

A. On question 1247 we wrote; Many contemporary Poskim quote Shemiras Shabbos Kehilchoso (16: 24) that permits playing with the Slider Number puzzle as a proof that the Rubik Cube should also be allowed. The Slider Number is a game consisting of (usually) fifteen movable, numbered squares set in a framed board the size of sixteen such squares, and rearranging the squares by moving them about within the framed board.
Horav Shlomo Miller’s Shlit’a opinion on both games is to be stringent. Although borer (the prohibited melacha of choosing), does not apply when you choose the desirable part (oichel) from the non-desirable (p’soiles), he maintains that this refers only when it is used immediately and not when it is only a part of a large sequence of algorithms that will create an eventual desirable oichel.
As far as taking apart and reassembling the cube on Shabbos, since this procedure is not commonly and constantly done, there will be likely an issur of tikun monno or fixing and completing a utensil. The above “solving” may be restricted even on weekdays, if it involves deception and g’neivas daas.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a