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Path sum: three ways

Problem 82

Published on Friday, 5th November 2004, 06:00 pm; Solved by 10885

NOTE: This problem is a more challenging version of Problem 81.

The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to 994.


13167323410318
20196342965150
630803746422111
537699497121956
80573252437331

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 left column to the right column.