Solution

sol.asm

_DATA SEGMENT
TriTable \
   BYTE 64
   BYTE 45,63
   BYTE 75,09,91
...et cetera
_DATA ENDS
   mov ebx, 0FFFFFFh ; path ;)
   xor ebp, ebp ; max total
next:	mov ecx, ebx
   xor edx, edx
   xor edi, edi
   shl ecx, 32-24
   mov esi, 0
@@:	inc esi
   shl ecx, 1
   movzx eax, [TriTable][edx]
   adc edx, esi
   add edi, eax
   cmp esi, 25
   jne @B
   ; max path total
   cmp ebp, edi
   cmovc ebp, edi
   dec ebx
   jns next