**From New Scientist #1421, 13th September 1984** [link]

The heads of eight colleges are four married couples. The colleges are so sited that the chapel towers of all are visible from the towers of all the others. To ensure that the bedrock on which all are built is not shifting, each head daily at noon ascends his tower and checks the range and bearing of each of the others. It is interesting, is it not, that in doing so he or she never has to traverse his sextant by *less* than a quarter of a right-angle — nor of course by more than two right angles.

Each male head is a different distance from his wife. Mrs *B* is due east of Mr *B*, while Mrs *A* is due southwest of Mr *A*. Mr *D* is closer to Mrs *D* than Mr *C* to Mrs *C*.

Through what angle must Mr *D* turn his sextant in traversing from Mr *C* to Mrs *C*?

[enigma274]

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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).