I wrote a mathematical Olympiad the other day and there was one question that I could not work out. The question was If ab = 1, bc =2, cd =3, de =4 and ea = 6, what does a + b + c + d +e =

It was a multiple choice and the answers were : 43/6; 47/6; 49/6; 53/6; 61/6 The correct answer was 61/6, but how can do you get to that answer?