MathDB

A bug starts at a vertex of a grid made of equilateral triangles of side length

1

. At each step the bug moves in one of the

6

possible directions along the grid lines randomly and independently with equal probability. What is the probability that after

5

moves the bug never will have been more than

1

unit away from the starting position?

<span class='latex-bold'>(A)</span>\ \frac{13}{108} \qquad<span class='latex-bold'>(B)</span>\ \frac{7}{54} \qquad<span class='latex-bold'>(C)</span>\ \frac{29}{216} \qquad<span class='latex-bold'>(D)</span>\ \frac{4}{27} \qquad<span class='latex-bold'>(E)</span>\ \frac{1}{16}

Problem Statement