A road network as shown in the figure connect four cities. In how many ways can you start from any city (any A) and come back to it without travelling on the same road more than once?

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Solution

The correct option is A $6$
Only 6 ways are possible. If you start with A:
1. 3 cases where you take 3 triangles having A as vertex
2. 3 cases when you take 4 sided polygon with A as vertex.
No other cases. Options are wrong.

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