Hi everyone

I'm Sirmojy, a mechanical engineer. I'm interested in mechanics, especially computational dynamics. But, my favorite work is computer programming. I have a good knowledge in C++ programming for Windows.

Also, I’m very interested in cross-sums puzzles. I try them whenever I see one. A few months ago, I decided to search the internet for any resources about these puzzles. But I was unable to find any good resources on this topic. So, I thought it is a good idea to have a program for generation of cross-sums puzzles. I started to design and develop such a program. The first part was the table generator. I developed it to generate random tables of given size. The next step was filling the table with random digits. I did it so, but I faced a problem. I tried to solve it, but was unable to find a good solution. Therefore, decided to share it here. Maybe someone can give me a good solution. I must mention that this is a completely free software, named MojiCS.

Now, let’s describe the problem:

How can I fill a given table with random digits to make sure that it has one and only one solution? In fact, since I fill the table with some digits, so, there exists at least one solution. But, how can it be guaranteed to be the only possible solution? I guess this needs some knowledge on linear algebra to be solved.

As an example, assume that my table generator component, has generated the following table:

Now, it’s time to fill it with some digits. For example, it can be filled as:

Therefore, the puzzle looks like this:

But, if you try to solve it, you will see that there is more than one solution for this puzzle. Here are 3 possible solutions:

The left one is my initial filling. The second one is a little different from the first; and the third one differs in all digits.

As another example, consider the following table:

If you try to solve it, you will see that there is only one solution, which is as below:

I hope these help you to understand the problem. Any comments are highly appreciated. Please feel free to contact me. You can download my program from here. Thanks a lot and excuse me for my poor English writing.