For any real number t , let [ t ] denote the largest integer t . Suppose that N is the greatest integer such that [ [ [ N ] ] =4 . Find the sum of digit of N .

Step-by-step solution

aligned & [ [ N ] ]=4 & 4 [ N ] < 5 & 16 [ [ N ] ] < 25 & 16 [ N ] < 25 & 256 [ N ] < 625 & 256 N < 625 & (256)^2 N < (625)^2 & N_ max. =390624 & sum of digit =24 Ans. aligned