We are given a partially filled grid with some specific numbers and an asterisk '' in position (5, 3) (row 5, column 3). Our goal is to determine the value of '' based on the given numbers in the grid.
To begin, let's observe the grid:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
& & & & 63 & & 88 \\
\hline
& & & 9 & & 25 & \\
\hline
& & 24 & & 16 & & \\
\hline
& 49 & & 13 & & & \\
\hline
10 & & * & & & & \\
\hline
& 9 & & & & & \\
\hline
\end{array}
\][/tex]
We need to identify any possible patterns or relationships between the numbers provided in the grid. However, due to the limited data,
1. Column and Row Sums: Attempting to calculate the sum for any row or column is inconclusive due to the missing numbers in the respective rows and columns.
2. Patterns: There seems to be no consistent arithmetic or geometric pattern that aligns the given numbers.
Given these observations, it is evident that we do not have enough information to determine the value of '*'. The relationships between the given numbers do not yield a discernible pattern or sum combinations that help in identifying the unknown value.
Thus, with the provided data and the absence of any clear arithmetic or logical pattern that ties the given numbers together, we conclude that:
[tex]\[
\boxed{\text{The value of '*' cannot be determined with the given data.}}
\][/tex]
