13. A multiplication table of the numbers 1 to 10 is shown. What is the sum of all the odd products in the complete table?
\begin{tabular}{c|ccccc}
$\times$ & 1 & 2 & 3 & $\cdots$ & 10 \\
\hline 1 & 1 & 2 & 3 & $\cdots$ & 10 \\
2 & 2 & 4 & 6 & $\cdots$ & 20 \\
$\vdots$ & $\vdots$ & & & & $\vdots$ \\
10 & 10 & 20 & 30 & $\cdots$ & 100
\end{tabular}
SolUTion
625

The odd numbers in the table are all the products of two of the odd numbers $1,3,5,7,9$. So their sum is $(1+3+5+7+9)(1+3+5+7+9)=25^{2}=625$.