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for what value of x it will have maximum number of minimum spanning trees ? what is the number of minimum spanning trees

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According to me, the value of x = 5. Therefore maximum number of MST = 2. Because, if you place any value of x less than 5, you will have to choose that path to reach the rightmost node. While for any value greater than 5, you will have to choose the bottom edge to reach the right most node. But if you put x = 5, you can either choose the top edge or the bottom edge to reach the right most node.

Therefore, Answer = 2.

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