Have you done any 'graph' problems? that is node-vector stuff.
You should be able to come up with a greedy algorithm that looks at the largest number in each row and tries to match with the largest on the row up and down - like the inverse of Djikstra (sp?)
Actually, you probably want to find largest pairs, then try to join them into a link from the top to the bottom eg in the first rom you have
"from one to two max is 75 + 95" so we store (1, 1, 2, 1, 180)
(row one item one and row two item 1 gives 180)
Then "From two to three max is 64 + 82" giving (2, 2, 3, 3, 146)
Looking back, we can't match these two, so you need to either decide to add
(1,1,2,2,75+64) so you can join them to make (1,1,3,3,75+64+146) or select the next largest from row 2 to 3.
Not perfect, but drop us a line if you refine it.