Sunday Times Teaser 2817 – Our Secret

by Victor Bryant

Published: 18 September 2016 (link)

Eight friends joined a very secret society and each was given a different membership number between 70 and 100. The friends are Bec, Cal, Doc, Ian, Jon, Luv, Rev and one other – and I am not willing to divulge his common three-letter name. But I can tell you that his membership number is 84.   Also, Bec’s membership number is the highest of the eight. The friends noticed that, for any pair of them, their names had at least one letter in common if and only if their membership numbers had a common prime factor.

(a) What was Ian’s membership number?

(b) What was the name of the eighth friend?