Mine Inspection

Answer :

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.

Math Genius