package require Tcl 8.6

proc maxTrianglePathSum {definition} {
    # Parse the definition, stripping whitespace and leading zeroes.
    set lines [lmap line [split [string trim $definition] "\n"] {
	lmap val $line {scan $val %d}
    }]
    # Paths are bit strings (0 = go left, 1 = go right).
    # Enumerate the possible paths.
    set numPaths [expr {2 ** [llength $lines]}]
    for {set path 0; set max -inf} {$path < $numPaths} {incr path} {
	# Work out how much the current path costs.
	set sum [set idx [set row 0]]
	for {set bit 1} {$row < [llength $lines]} {incr row} {
	    incr sum [lindex $lines $row $idx]
	    if {$path & $bit} {incr idx}
	    set bit [expr {$bit << 1}]
	}
	# Remember the max so far.
	if {$sum > $max} {set max $sum}
    }
    return $max
}

puts [maxTrianglePathSum {
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
}]
# Reading from a file is left as an exercise…