The diagram below shows a network of roads in a small village with the weights indicating the distance of each road, in metres, and junctions indicated with letters. 
Musab is required to deliver leaflets to every house on each road. He wishes to minimize his total distance.
Musab starts and finishes from the village bus-stop at A. Determine the total distance Musab will need to walk.
Odd vertices are A, B, D, H A1
Consider pairings: Note: Award (M1) if there are four vertices not necessarily all correct.
AB DH has shortest route AD, DE, EB and DE, EH, so repeated edges Note: Condone AB in place of AD, DE, EB giving .
AD BH has shortest route AD and BE, EH, so repeated edges
AH BD has shortest route AD, DE, EH and BE, ED, so repeated edges
Note: Award A1 if only one or two pairings are correctly considered. so best pairing is AD, BH weight of route is therefore
Instead of having to catch the bus to the village, Musab's sister offers to drop him off at any junction and pick him up at any other junction of his choice. Explain which junctions Musab should choose as his starting and finishing points.
least value of the pairings is 19 therefore repeat AD
R1 B and H A1 Note: Do not award R0A1.
