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The following undirected network consists of seven vertices and twelve edges with a total weight of \(243\). The same network can be represented by the matrix below. A B C D E F G A - 16 12 21 - - - B 16 - - 17 20 - - C 12 - - 28 - 31 - D 21 17 28 - 18 19 23 E - 20 - 18 - - 11 F - - 31 19 - - 27 G - - - 23 11 27 - However, it is possible to optimize the network by removing some edges and still e..
The Fibonacci sequence is defined by the recurrence relation: \({\rm F}_n = {\rm F}_{n-1} + {\rm F}_{n-2}, \) where \({\rm F}_1 =1 \) and \({\rm F}_2 = 1\) It turns out that \(\rm F_{541}\), which contains \(113\) digits, is the first Fibonacci number for which the last nine digits are \(1-9\) pandigital (contain all the digits \(1\) to \(9\), but bot necessarily in order). And \(\rm F_{2749}\),..
If a box contains twenty-one colored discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen that the probability of taking two blue discs, \(\rm P(BB)=\dfrac{15}{21} \times \dfrac{14}{20} = \dfrac{1}{2}\) The next such arrangement, for which there is exactly \(50%\) chance of taking two blue discs at random, is a box containing eighty-five blu..