Finding the AMC 8 Path
Source: 2017 AMC 8 #15
November 22, 2017
AMC 8
Problem Statement
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 allows only 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.
[asy]
fill((0.5, 4.5)--(1.5,4.5)--(1.5,2.5)--(0.5,2.5)--cycle,lightgray);
fill((1.5,3.5)--(2.5,3.5)--(2.5,1.5)--(1.5,1.5)--cycle,lightgray);
label("", (1, 0));
label("", (2, 0));
label("", (3, 0));
label("", (0, 1));
label("", (1, 1));
label("", (2, 1));
label("", (3, 1));
label("", (4, 1));
label("", (0, 2));
label("", (1, 2));
label("", (2, 2));
label("", (3, 2));
label("", (4, 2));
label("", (0, 3));
label("", (1, 3));
label("", (2, 3));
label("", (3, 3));
label("", (4, 3));
label("", (1, 4));
label("", (2, 4));
label("", (3, 4));[/asy]