A network of roads connects locations T, O, W, N, and S as shown. How many different routes are there to travel from T to W along the given roads (line segments) without retracing any part of the route or going to any town more than once per route?

A network of roads is a blueprint of how each towns or cities are linked by a path or road. So that in the given question, the different routes to travel from T to W with respect to the given conditions are:

i. TNW

ii. TSW

iii. TOW

iv. TOSW

v. TNSW

vi. TNSOW

vii. TOSNW

viii. TSNW

ix. TSOW

There are nine (9) different routes from T to W.

A route is either a path or road that links or connects two or more villages, cities or towns. Thus, a person can travel or be conveyed from one town to the other, or city (village) to another, depending of the road network. Road network is the cobweb of connecting roads among cities.

Considering the network of roads in the given diagram and the conditions for travelling from T to W, then the number of routes is nine. And these routes are:

TNW
TSW
TOW
TOSW
TNSW
TNSOW
TOSNW
TSOW
TSNW

Given that no part of the route should be retraced or going to any town more than once per route.

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