A correct solution was also received from Felice Kelly. A further correct solution was also received from Jeff Duggins.

My apologies to the several problem solvers who wrote to say that the problem had given them a headache!

There are two solutions. Many thanks to Ray Kremer for the sketches below. Some observations from Nathan Pauli follow.

There are two ways that B could rotate through a right angle, either upward or downward. If rotated upward, the final orientation of the plates is as on the right; if rotated downward, as on the left.

It's interesting to note that two of the hinges move some during the rotation, but return to their original orientation. All the others move at right angles. The two that return to their original orientation are C-d and A-F.

You can easily build such a contraption using Legos. You'll find that B cannot be rotated in a complete circle with respect to A. It'll stop somewhere around 135 degrees either way, possibly smaller with a construction that doesn't jiggle as much as the Lego's do.

Let me offer one further question: What is the largest angle through which plate B can be rotated?

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