# Problem 83: Path sum: four ways
NOTE: This problem is a significantly more challenging version of
Problem 81. In the 5 by 5 matrix below, the minimal path sum from the
top left to the bottom right, by moving left, right, up, and down, is
indicated in bold red and is equal to 2297. \$\$ \\begin{pmatrix}
\\color{red}{131} & 673 & \\color{red}{234} & \\color{red}{103} &
\\color{red}{18}\\\\ \\color{red}{201} & \\color{red}{96} &
\\color{red}{342} & 965 & \\color{red}{150}\\\\ 630 & 803 & 746 &
\\color{red}{422} & \\color{red}{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
moving left, right, up, and down.