Q. A recent kuntros in Eretz Yisroel was published saying that playing a Rubik cube on Shabbos is a problem of borer. What is Rav Miller position on the issue? Thank you!

A. On request, the name of the Posek who is stringent in the use of the Rubik cube was provided and it is Horav Mendel Fuchs Shlit’a, a Mo”Tz of the Eida Chareidis.
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 also to be stringent. Although borer 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 create an eventual desirable oichel.

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