Backtracking can also be used to solve many mathematical puzzles such as Cryptogram and

Sudoku. There is a variant of Sudoku, that has not yet found a published solution using

backtracking in the net. This means that you do not need to worry about classmates gaining

an unfair advantages by downloading and adapting someone else's solution.

A puzzle consists of a rectangular grid of cells. It is divided into blocks each containing up to

five cells. In the task below, they are indicated by different colors. In the solution, each cell

contains a digit from $1$ to $n,$ with $n$ being the number of cells in the block. So$,$ a single cell

block contains only a cell with $1,$ a two$-$cell block contains one cell with $1$ and one with $2,$ and

so on$.$ The same digit is not allowed to appear in a neighboring cell, not even diagonally. For

example, the contents of cells $(1,1),(2,1),(3,1),(1,2),(3,2),(1,3),(2,3),$ and $(3,3)$ cannot be $4.$

Some cell contents are already given.

Use the recursive backtracking scheme from class to solve the following problem: