No Adjacent Colors on Cube

Geometry Level 5

A Rubik's Cube is turned multiple times such that any two adjacent faces of two adjacent cublets have different colors. Find the minimum number of turns of the Rubik's Cube to achieve this.

Details and Assumptions

A turn on a Rubik's cube is either turning a face \(90^{\circ}\), \(180^{\circ}\), or \(270^{\circ}\) clockwise.

The Rubik's cube starts at its solved state.

In the picture below, \(1\) is adjacent to \(2\), \(3\), and \(4\). However, \(2\), \(3\), and \(4\) are pairwise non-adjacent.


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