## Path sum: two ways

### Problem 81

Published on Friday, 22nd October 2004, 06:00 pm; Solved by 21423; Difficulty rating: 10%In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by **only moving to the right and down**, is indicated in bold red and is equal to 2427.

$$
\begin{pmatrix}
\color{red}{131} & 673 & 234 & 103 & 18\\
\color{red}{201} & \color{red}{96} & \color{red}{342} & 965 & 150\\
630 & 803 & \color{red}{746} & \color{red}{422} & 111\\
537 & 699 & 497 & \color{red}{121} & 956\\
805 & 732 & 524 & \color{red}{37} & \color{red}{331}
\end{pmatrix}
$$

Find the minimal path sum, in matrix.txt (right click and "Save Link/Target As..."), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.