Answer
For an open organ pipe, the harmonics are
$\frac{v}{2L}, \frac{2v}{2L}, \frac{3v}{2L}, \frac{4v}{2L}, .........$
For a closed organ pipe, the harmonics are
$\frac{v}{2L}, \frac{3v}{2L}, \frac{5v}{2L}, \frac{7v}{2L}, ..........$
We can see that the harmonics of an open organ pipe and a closed organ pipe can never be equal if both are of the same length since none of the harmonics of both pipes are equal.
Work Step by Step
For an open organ pipe, the harmonics are
$\frac{v}{2L}, \frac{2v}{2L}, \frac{3v}{2L}, \frac{4v}{2L}, .........$
For a closed organ pipe, the harmonics are
$\frac{v}{2L}, \frac{3v}{2L}, \frac{5v}{2L}, \frac{7v}{2L}, ..........$
We can see that the harmonics of an open organ pipe and a closed organ pipe can never be equal if both are of the same length since none of the harmonics of both pipes are equal.
