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Let Q be the cube with the set of vertices { (x 1 , x 2 , x 3 )  R 3  : x 1 , x 2 , x 3  {0, 1} } . Let F be the set of all twelve lines containing the diagonals of the six faces of the cube Q. Let S be the set of all four lines containing the main diagonals of the cube Q; for instance, the line passing through the vertices (0,0,0) and (1,1,1) is in S. For lines  1 and  2 , let d(  1 ,  2 ) denote the shortest distance between t hem. Then the maximum value of d(  1 ,  2 ), as  1 varies over F and  2 varies over S, is

1. 6 1
2. 8 1
3. 3 1
4. 12 1

Correct answer: 6 1

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