\(\ 1\).(\(\ 16\) marks)Consider a chessboard of size \(\ 8\) units\(\ \times8\) units (i.e., each small square on the board has a side length of \(\ 1\) unit).Let \(\ S\) be the set of all the \(\ 81\) vertices of all the squares on the board.What is the number of...

Problem Let \( g: \mathbb{N} \to \mathbb{N} \) with g(n) being the product of the digits of n. Prove that \( g(n) \le n \) for all \( n \in \mathbb{N} \) Find all \( n \in \mathbb {N}\) for which \( n^2 -12n + 36 = g(n) \) DIscussion...

This is a Test of Mathematics Solution Subjective 175 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I....