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Note : In your question, it will be 15 rather than 16 . In solid square, soldiers will be across the area of the square and in hollow square, they will be along perimeter of the square . Let' n' be the number of soldiers in the front row when arranged in a square . Hence total number of soldiers = 4 \times n = 4 n . . . . . . . . . . (i) The number of soldiers in the front row when arranged in solid square = (n - 15) \Rightarrow The total number of soldiers = (n - 15) (n - 15) = {(n - 15)}^{2} \Rightarrow The total number of soldiers = n^{2} - 30 n + 225 . . . . . . . . . . . . . (ii) By first and second n^{2} - 30 n + 225 = 4 n \Rightarrow n^{2} - 30 n - 4 n + 225 = 0 \Rightarrow n^{2} - 34 n + 225 = 0 \Rightarrow n^{2} - 25 n - 9 n + 225 = 0 \Rightarrow n (n - 25) - 9 (n - 25) = 0 \Rightarrow (n - 9) (n - 25) = 0 Hence n = 25 or n = 9 But n = 9 is not possible as n - 15 will be negative . Hence n = 25 total number of soldiers = 4 n = 4 \times 25 = 100 (Answer)

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