Finding maximum paths
GolfScript - 49 Nabb enhanced characters
51 characters
50 strictly and utterly necessary characters + 3 slackers that only did the job of 1
56 mostly redundant characters
n%{~]}%.zip{{0@+\{\.1&gt;\3&lt;$-1=@+}%\;}*$-1=\}2*' '@

51 solution:
n%{~]}%.zip{(\{0@+\{\.1&gt;\3&lt;$-1=@+}%\}%;$-1=\}2*' '@

53 solution:
n/{~]}%);.zip{(\{0@+\{\.1&gt;\3&lt;$-1=@+}%\}%;$-1=\}2*' '@
             a8_b9___c10___11______12 13      14_

The method works on two lines at a time, one containing the maximum sums reached at each point, and one containing the next line.
a/14: Repeat twice, once for each result.
8: Take the first line from the input and switch it behind the input array, this in now the first set of maximum sums.
b/13: Iterate over each remaining line in the array.
9: Put 0 at the beginning of the maximum sums.
c/12: Iterate over each element of the line.
10: Make a copy of the maximum sums with the first element removed.
11: Take the first 3 elements of the maximum sums, sort them and add the largest to the current element of the line.
56 solution:
n/{~]}%);.zip{1,99*\{{\.1&gt;\3&lt;$-1=@+}%0\+\}%;$-1=\}2*' '@
1________2___ 3____ 4______________________5_____ 6_7___

1: From input to array of arrays in 9 characters, actually it could have been done with just 1, but I broke that key so this will have to do.
2: 4 characters just to make a transposed copy.
3: Array of 99 0s in 5 characters, it could probably be done in a way smarter fashion, but I smoke too much weed to figure how.
4: Overly complicated double loop that iterate over every single element of the input and does some fuzzy logic or something like that to produce the result. Nabb will probably make something equivalent in around 3½ characters.
5: By now the result is there, inside an array that is, this silly piece of code is just there to get it out (and junk a piece of leftovers (and switch the result into place)).
6: This is a command so simple that its character count would probably be negative in an optimal solution.
7: At this point the program is really done, but due to sloppiness in the preceding code the output is in the wrong order and lacks a space, so here goes a few more bits down the drain.