2017 AMC 8
Complete problem set with solutions and individual problem pages
In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path only allows moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.
- A.
- B.
- C.
- D.
- E.
Solution 1
Notice that the is adjacent to s, each is adjacent to s, and each is adjacent to 's. So for each , there are s, and for each , there are s, and for each , there are s. Thus, the answer is
Solution 2
There are three different kinds of paths that are on this diagram. The first kind is when you directly count , , in a straight line. The second is when you count , turn left or right to get , then go up or down to count and . The third is the one where you start with , move up or down to count , turn left or right to count , then move straight again to get .
There are paths for each kind of path, making for paths.
