Problem Suppose we have \( n \) numbers \(x_{1},x_{2}, \cdots x_{n} \), in that order. Compute the number \(C_{n} \) of ways of positioning the brackets to multiply the product of the \(n\) numbers, without changing the given order. HintIf \(n=2\) we have only one case: \((x_{1} x_{2})\) If \(n=3\) Read more…
Problem Suppose we compose numbers using only the digits in the set \( \{1,2,3\}\). Compute the total numbers with the following properties: having length \(n\) beginning and ending with the digit \(\displaystyle 1\) the adjacent digits are always different from each other We indicate this number with \(Z_{n}\). For example Read more…
Problem Let’s consider the following \(5 \times 5\) matrix of positive integers: \[ \begin{pmatrix} d & 2d & 3d & ? & 5d \\ 11 & ? & ? & ? & ? \\ ? & 32 & ? & ? & ? \\ ? & ? & ? & Read more…
A prime number is an integer greater than 1 which is divisible only by 1 and by itself. An integer that is not prime is called composite. Each integer greater than 1 is divisible by at least one prime number. The study of integers and their properties began with the Greeks (Pythagoras, Euclid,…), Read more…
A useful tool to understand the architecture of modern platforms for the development of video games is the layered model. Complex systems are characterized by a set of components (even hundreds or thousands) that interact with each other. The layered model consists of dividing the system into various levels of abstraction: each Read more…