A Tenner Grid is a Mathematical puzzle that consists of a rectangular grid of width ten cells. The goal is to fill in the grid so that each row contains the numbers 0 to 9. Numbers must not be repeated in rows. In columns the numbers may be repeated and the numbers in a column must add up to a given target sum. Therefore, the bottom numbers give the sum of the numbers in column. The digits in contiguous cells (even diagonally contiguous cells) must be different.

The rules of Tenner Grids math puzzles:

1. Numbers appear only one time in a row.

2. Numbers can be repeated in columns.

3. Numbers in the columns must add up to the given sums.

4. Numbers in connecting cells must be different.

Like this:

TO DO:

1) Write an AI program to generate and solve the game Tenner Grid by modeling it as constraint satisfaction problem. Your program must solve a randomly generated Tenner Grid Puzzle in Simple backtracking, Backtracking with the MRV heuristic, Forward checking, Forward checking with MRV heuristic. You can configure your program to either solve 10 by 3 Tenner Grid Puzzles, 10 by 4 Tenner Grid Puzzles, 10 by 5 Tenner Grid Puzzles, or 10 by 6 Tenner Grid Puzzles.

2) For each algorithm, show the initial state (randomly generated state), final CSP Tenner variable assignments, number of variable assignments and number of consistency checks, the solution found (final state), and time used to solve the problem.

3) Conduct a comparison of various CSP algorithms (Backtracking, BT+MRV. Forward Checking, and FC+MRV) on Tenner Grid problem.

4) Analyze the median number of consistency checks (over five runs) required to solve the problem and show the results in term of which algorithm is better to solve the problem.

Requirements:

1) Source Code in Python or Java.

2) Explanation of Code.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{2}{|c|}{ Example of 10 by 4 Tenner Grid Puzzles } \\ \hline \hline & 6 & 2 & 0 & & & & 8 & 5 & 7 \\ \hline & 0 & 1 & 7 & 8 & & & & 9 & \\ \hline & 4 & & & 2 & & 3 & 7 & & 8 \\ \hline 13 & 10 & 8 & 7 & 19 & 16 & 11 & 19 & 15 & 17 \\ \hline \end{tabular} Solution \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline 4 & 6 & 2 & 0 & 9 & 1 & 3 & 8 & 5 & 7 \\ \hline 3 & 0 & 1 & 7 & 8 & 6 & 5 & 4 & 9 & 2 \\ \hline 6 & 4 & 5 & 0 & 2 & 9 & 3 & 7 & 1 & 8 \\ \hline 13 & 10 & 8 & 7 & 19 & 16 & 11 & 19 & 15 & 17 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline & & 1 & & 3 & 8 & 6 & 9 & & 2 \\ \hline 6 & 2 & & & 1 & & & 7 & 4 & 3 \\ \hline 7 & 4 & 5 & & 0 & 6 & & & 8 & \\ \hline & & 8 & & 4 & 9 & 5 & 7 & & \\ \hline 7 & 9 & 1 & 0 & & & 4 & 8 & 5 & 2 \\ \hline 26 & 20 & 15 & 27 & 14 & 35 & 21 & 34 & 23 & 10 \\ \hline \end{tabular} Solution \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline 4 & 5 & 1 & 7 & 3 & 8 & 6 & 9 & 0 & 2 \\ \hline 6 & 2 & 0 & 8 & 1 & 9 & 5 & 7 & 4 & 3 \\ \hline 7 & 4 & 5 & 9 & 0 & 6 & 1 & 3 & 8 & 2 \\ \hline 2 & 0 & 8 & 3 & 4 & 9 & 5 & 7 & 6 & 1 \\ \hline 7 & 9 & 1 & 0 & 6 & 3 & 4 & 8 & 5 & 2 \\ \hline 26 & 20 & 15 & 27 & 14 & 35 & 21 & 34 & 23 & 10 \\ \hline \end{tabular}