Exact value and rigidity of the 2 times3 magic rectangle
The 2x3 magic rectangle is a nonlocal game where players match entries with incompatible parity rules. This paper proves its exact quantum value is (1+sqrt(2/3))/2 and classifies all optimal strategies in any finite local dimension. It shows that optimal strategies require a specific four-dimensional entangled state and links the game to bounds on magic-square scores and three-bit random access codes.