MathDB

Many calculators have a reciprocal key

\boxed{\frac{1}{x}}

that replaces the current number displayed with its reciprocal. For example, if the display is

\boxed{00004}

and the

\boxed{\frac{1}{x}}

key is depressed, then the display becomes

\boxed{000.25}

. If

\boxed{00032}

is currently displayed, what is the fewest number of times you must depress the

\boxed{\frac{1}{x}}

key so the display again reads

\boxed{00032}

\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5

Problem Statement