2024 Fermat Problem 21

A 3 \times 3 table starts with every entry equal to 0 and is modified using the following steps:

(i) adding 1 to all three numbers in any row;

(ii) adding 2 to all three numbers in any column.

After step (i) has been used a total of a times and step (ii) has been used a total of b times, the table appears as shown. What is the value of a + b?

\begin{array}{|c|c|c|}\hline 7 & 1 & 5 \\ \hline 9 & 3 & 7 \\ \hline 8 & 2 & 6 \\ \hline\end{array}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.