To help you with the addition and filling in the missing values in the grid, I need to first analyze the structure of the table. Here's what I can observe:

1. Grid Layout: The table consists of 5 rows and 5 columns.
2. Numbers Present:
   • The rightmost column contains the numbers: 25, 50, 70, 85, and 95.
   • The bottom row contains the numbers: 35, 55, 70, 80, and 85.

Based on this layout, the missing values should add up to form these totals, while ensuring no repeated values are used within the table.

Plan:

• We will add numbers into the empty cells such that the sum of each row matches the number at the end of the row.
• Similarly, the sum of the numbers in each column must match the numbers at the bottom.

I will proceed by solving this step by step. Let me calculate that now.I have initialized the grid for solving. Now I will fill in the values step by step, ensuring that the sum of each row matches the right-side values and the sum of each column matches the bottom-side values, while making sure no values are repeated.

Let me calculate that now.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through solving the puzzle manually, or provide some insights into how you could approach it? Let me know if you need further help with this problem!

Here are some related questions that might help you think through the puzzle:

1. How do you approach balancing row and column sums in a matrix?
2. What strategies can be used to avoid repetition when filling a grid with constraints?
3. How would you adjust your grid if only a subset of values is available?
4. How can algebraic methods help in solving grid puzzles with multiple conditions?
5. What are some common techniques for solving optimization problems involving sums?

Tip: Start with the rows and columns that have the smallest sum requirements, as they may limit the values you can choose for other rows and columns.