Problem $1$Classic AI search algorithms are very good at finding solutions to some of the mathematical puzzles involving numbers and geometric figures. Problems such as moving or removing matches to form figures, magic squares, SUDOKU, among others, can be solved by a computer very efficiently and faster than a human being.Consider the example of the magic triangle of $6$ numbers, in which the numbers $1$ to $6$ must be placed in the six positions indicated in the following figure, in such a way that all the sides of the triangle add up to $10.$In order to solve the magic triangle problem, we want to use uninformed search algorithms. To do this, it is considered that it starts with an empty triangle, and the six numbers are placed one by one, starting with $1,$ until all $6$ spaces are filled. That is$,$ when selecting the space for number $1,$ we proceed to select the space for number $2$ among the five remaining circles, and so on$.$ If after placing the $6$ numbers you have a triangle where its three sides add up to $10,$ you have a valid solution.Formulate the search problem you want to solve, formally describe the problem.Solve the problem $"$by hand" by developing search trees at least $4$ levels deep:width search,depth search.What is the path to the solution so far in each tree?Which algorithm solves the problem faster? Why could such an algorithm be an improvement for this problem?