Problems(1)
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("8", (1, 0));
label("C", (2, 0));
label("8", (3, 0));
label("8", (0, 1));
label("C", (1, 1));
label("M", (2, 1));
label("C", (3, 1));
label("8", (4, 1));
label("C", (0, 2));
label("M", (1, 2));
label("A", (2, 2));
label("M", (3, 2));
label("C", (4, 2));
label("8", (0, 3));
label("C", (1, 3));
label("M", (2, 3));
label("C", (3, 3));
label("8", (4, 3));
label("8", (1, 4));
label("C", (2, 4));
label("8", (3, 4));[/asy]<spanclass=′latex−bold′>(A)</span>8<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>24<spanclass=′latex−bold′>(E)</span>36 AMC 8