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Question

A road map connecting to the colonies A, B, C, D and E is shown in the figure below. Design the route starting from any colony of your choice so that you will have to walk on each of the seven routes once and only once. The starting point and the end point may not be the same. From how many points, can such route be started?

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A
Two
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B
None
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C
One
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D
Three
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Solution

The correct option is A Two
For this question, we can take all points one by one.

Such route started from Point A: Yes it exists, route ACDEBDAB, etc.
Such route started from Point B: Yes it exist , route BADEBDCA, etc.
Such route started from Point C: No it does not exist.
Such route started from Point D: No it does not exist.
Such route started from Point E: No it does not exist.

So, such route is started only from two points i.e., A and B. Hence, the correct answer is option(3)i.e. Two.

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