SOLUTION: An SF path starts at S, follows along the edges of the squares, never visits any vertex more than once, and finishes at F. An example of an SF path is shown. (A vertex is a poin

Algebra ->  Permutations -> SOLUTION: An SF path starts at S, follows along the edges of the squares, never visits any vertex more than once, and finishes at F. An example of an SF path is shown. (A vertex is a poin      Log On


   

Question 1178620: An SF path starts at S, follows along the edges of the
squares, never visits any vertex more than once, and finishes
at F. An example of an SF path is shown. (A vertex is a
point where two or more of the squares’ edges meet.)
This is the question (I took a screenshot):
https://drive.google.com/file/d/1PBiwLlK971wMDwIjFABNOb3QhBzEJhNs/view?usp=sharing
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Consider the "center" of the array of squares, as shown here:
             f -------- g -------- X
             |          |          |
             |          |          |
             |          |          |
             |          |          |
  X -------- c -------- d -------- e
  |          |          |
  |          |          |
  |          |          |
  |          |          |
  X -------- a -------- b

  vertex     # of paths to that vertex
  ----------------------------------------
    a       C(19,0) = 1
    b       C(20,0) = 1
    c       C(19,1) = 19
    d       = b+c = 1+19 = 20
    e       = d = 20
    f       = c = 19
    g       = d+f = 39

Any SF path passes through exactly one of vertices e and g.

# paths g to F: C(19,0) = 1
# paths e to F: C(18,1) = 18

# paths S to F: 39*1 (through g) plus 20*18 (through e) = 39+360 = 399

ANSWER: 399 SF paths