jmc

Starting with row $0$, the $k^{\text{th}}$ row has the numbers $$\left(\genfrac{}{}{0ex}{}{k}{0}\right),\left(\genfrac{}{}{0ex}{}{k}{1}\right),\left(\genfrac{}{}{0ex}{}{k}{2}\right),\dots ,\left(\genfrac{}{}{0ex}{}{k}{k}\right).$$For every number in the row except the first and last values to be even, $k$ must only have even factors, so it must be a power of $2$. Since the highest power of $2$ under $100$ is $2^6=64$, $\boxed{6}$ of the first 100 rows have only even numbers besides $1$.