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This Python program runs in 43ms

Solution:Mr D must turn his sextant through 90° in traversing from Mr C to Mrs C.There are four different solutions, one pair where the B’s are located at adjacent points, and another pair where the B’s have two points between them. In all cases the C’s are located on opposite ends of a diameter, so from any of the other points (including either of the D’s) the angle they subtend is a right angle (as the triangle formed is inscribed within a semicircle – Thales’ Theorem).