Enigma 274: College angles
19 April 2015
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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?