Starting from A, the inspector need only travel 36 furlongs if he takes
the following route: A to B, G, H, C, D, I, H, M, N, I, J, O, N, S, R,
M, L, G, F, K, L, Q, R, S, T, O, J, E, D, C, B, A, F, K, P, Q. He thus
passes between A and B twice, between C and D twice, between F and K
twice, between J and O twice, and between R and S twice--five
repetitions. Therefore 31 passages plus 5 repeated equal 36 furlongs.
The little pitfall in this puzzle lies in the fact that we start from an
even node. Otherwise we need only travel 35 furlongs.