For all natural n, an n-staircase is a figure consisting of unit squares, with one square in the first row, two squares in the second row, and so on, up to n squares in the nth row, such that all the left-most squares in each row are aligned vertically.
Let f(n) denote the minimum number of square tiles requires to tile the n-staircase, where the side lengths of the square tiles can be any natural number. e.g. f(2)=3 and f(4)=7.
(a) Find all n such that f(n)=n.
(b) Find all n such that f(n)=n+1. inductiongeometrygeometric transformationreflectionsymmetrycombinatorics unsolvedcombinatorics