There are 9 cities numbered 1 to 9. From how many cities the flight can start so as to reach the city 8 either directly or indirectly such the path formed is divisible by 3.

Assuming that you can't visit any city more than once and that I haven't missed any journeys the answer is 64961.

This consists of the journeys listed below. Only pathways where successive cities having a higher number are listed but these cities can obviously be visited in any order as long as City 8 is the last; eg from the four-city group the path 1-2-4-8 represents these trips also: 1-4-2-8, 2-1-4-8, 2-4-1-8, 4-1-2-8, and 4-2-1-8 meaning that, for the four-city group, the number of paths listed must be multiplied by 6 to give the actual total. Two-cities: (3) 1-8, 4-8, 7-8

## 9 Cities Numbered 1 to 9

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