How many paths spell MICROWAVE     M
   I I
  C C C
 R R R R
O X O O O
 W W W W 
  A A A
   V V V
    E E

Starting with the M on top and only moving one letter at a time down to the left or right, how many different paths from top to bottom spell MICROWAVE? However you cannot move to the "X". I understand this uses Pascal's triangle but I'm not sure where to go once I reach the "X" since, it needs to be skipped. I would really appreciate it if someone could help me with this problem.
    1
   1 1
  1 2 1 
 1 3 3 1
1 X 6 4 1
 W W 10 5
  A A A
   V V V
    E E

The work above is when I tried to solve this using Pascal's triangle, but as you can see above, I'm not sure which number to put after for "W".
 A: Originally I had an overcomplicated way, but since you brought up Pascal's triangle I will continue from there.
You are close to the answer, the final step you need is to write $X$ as $0$ simply, as there is "no way" to get to that square and of course no way to get out. You can then continue the Pascal's triangle:
    1
   1 1
  1 2 1 
 1 3 3 1
1 0 6 4 1
 1 6 10 5
  7 16 15
   23 31 15
    54 46

(If you want, you can add a "sink" at the end that collects both E's that will have a value of 100, but that's not necessary).
Finally, the answer is $54+46=100$.
A: Place a 1 on the M.
The Is both become 1s
The line of Cs become 121 - just like Pascal’s triangle. That’s because the number of ways of getting to a particular letter is the sum of the two above.
The line of Rs become 1331
The line of Os would become 14641 but one of them is forced (by the X) to be 0.
That makes a line that is 10641
The line of Ws is 1 6 10 5
The line of As is 7 16 15
The line of Vs is 23 31 15
I’ll leave the last line to you!
The final answer is the sum of the last two Es.
