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?

Aurora (student) (grd9)

middle

Hi Aurora,
From ab = 1 we have b = ^{1}/_{a}.

From bc = 2 we have c = ^{2}/_{b}, substituting b = ^{1}/_{a} we have that c = 2a.

From cd = 3 we have d = ^{3}/_{c}, substituting c = 2a we have that d = ^{3}/_{2a}.

From de = 4 we have e = ^{4}/_{d}, substituting d = ^{3}/_{2a} we have e = ^{8a}/_{3}.

Since ea = 6 and e = ^{8a}/_{3} we find ^{8a 2}/_{3} = 6, solving for a, we have a = ^{3}/_{2}.

From this b = ^{1}/_{a} = ^{2}/_{2}, c = 2a = 3, d = ^{3}/_{2a} = 1 and e = ^{8a}/_{3} = 4.

Add these numbers.

Andrei