Browse · MATH
Printjmc
counting and probability senior
Problem
On the -plane, the origin is labeled with an . The points , , , and are labeled with 's. The points , , , , , , , and are labeled with 's. The points , , , , , , , , , , , and are labeled with 's. If you are only allowed to move up, down, left, and right, starting from the origin, how many distinct paths can be followed to spell the word MATH?
Solution
From the M, we can proceed to four different As. Note that the letters are all symmetric, so we can simply count one case (say, that of moving from M to the bottom A) and then multiply by four.
From the bottom A, we can proceed to any one of three Ts. From the two Ts to the sides of the A, we can proceed to one of two Hs. From the T that is below the A, we can proceed to one of three Hs. Thus, this case yields paths.
Thus, there are distinct paths.
From the bottom A, we can proceed to any one of three Ts. From the two Ts to the sides of the A, we can proceed to one of two Hs. From the T that is below the A, we can proceed to one of three Hs. Thus, this case yields paths.
Thus, there are distinct paths.
Final answer
28